CECCO Namespace Reference

Provides a framework for error correcting codes. More...

Namespaces
namespace	details
	Contains implementation details not to be exposed to the user. Functions and classes here may change without notice.

Classes
class	SDMEC
	Symmetric Discrete Memoryless Erasure Channel (SDMEC) over any finite field 𝔽_q. More...
class	SDMC
	Symmetric Discrete Memoryless Channel — errors only, no erasures. More...
class	BEC
	Binary Erasure Channel — symbols are received correctly or marked erased. More...
class	BAC
	Binary Asymmetric Channel (Z-channel) — 0 is preserved; 1 flips to 0 with probability p. More...
class	NRZMapper
	Non-Return-to-Zero (NRZ) mapper for binary modulation. More...
class	BPSKMapper
	Binary Phase Shift Keying mapper — NRZMapper with a = 0, b = 2. More...
class	AWGN
	Additive White Gaussian Noise channel for complex-valued symbols. More...
class	BI_AWGN
	Binary-Input AWGN — fused NRZMapper + AWGN block. More...
class	NRZDemapper
	Non-Return-to-Zero (NRZ) hard-decision demapper. More...
class	BPSKDemapper
	BPSK hard-decision demapper — NRZDemapper with threshold 0. More...
class	LLRCalculator
	Log-Likelihood Ratio calculator for NRZ-over-AWGN soft demodulation. More...
class	DEMUX
	Field demultiplexer — expand 𝔽_E elements into 𝔽_S coefficient vectors/matrices. More...
class	MUX
	Field multiplexer — reconstruct 𝔽_E elements from 𝔽_S coefficients. More...
class	Code
class	EmptyCode
class	LinearCode
class	UniverseCode
class	ZeroCode
class	SimplexCode
class	SingleParityCheckCode
class	ExtendedCode
class	CodewordIterator
class	decoding_failure
class	HammingCode
class	RepetitionCode
class	GolayCode
class	GRSCode
class	RSCode
class	CordaroWagnerCode
class	LDCCode
class	RMCode
class	SubfieldSubcode
class	AlternantCode
class	BCHCode
class	GoppaCode
class	AugmentedCode
class	Enc
class	Dec
class	Encinv
class	Rationals
	Field of rational numbers ℚ = { p/q : p, q ∈ ℤ, q ≠ 0 } with selectable precision. More...
class	Fp
	Prime field 𝔽_p ≅ ℤ/pℤ More...
class	Ext
	Extension field 𝔽_{q^m} ≅ B[x]/(f(x)), constructed from a base field and an irreducible monic modulus polynomial. More...
class	Iso
	Single logical field unifying several pairwise-isomorphic representations. More...
class	Vector
	Vector v = (v₀, v₁, …, vₙ₋₁) over a CECCO::ComponentType. More...
class	Polynomial
	Univariate polynomial p(x) = a₀ + a₁x + … + aₙxⁿ over a CECCO::ComponentType. More...
class	Matrix
	Dense m × n matrix over a CECCO::ComponentType. More...
class	Embedding
	Functor representing the field embedding φ: SUBFIELD → SUPERFIELD, with reverse lookup. More...
class	Isomorphism
	Functor representing the field isomorphism φ: A → B between two same-size finite fields. More...
class	RNG
	Thread-local random number generator with shared seeding policy. More...
struct	Trellis
	Trellis with field-labelled edges between consecutive layers. More...

Concepts
concept	FieldType
	Concept for field types: full algebraic interface.
concept	FiniteFieldType
	Refines FieldType for finite fields 𝔽_{p^m}.
concept	SignedIntType
	Standard signed integers or InfInt for arbitrary precision.
concept	ReliablyComparableType
	Types whose operator== reflects mathematical equality.
concept	ComponentType
	Admissible component type for CECCO::Vector, CECCO::Polynomial, CECCO::Matrix.
concept	BelongsTo
	T is identical to at least one of Types....
concept	Isomorphic
	A and B are finite fields of the same size (and thus isomorphic).
concept	SubfieldOf
	SUBFIELD ⊆ SUPERFIELD as constructed in this library (Iso paths included).
concept	ExtensionOf
	Inverse of SubfieldOf: ExtensionOf<S, E> iff SubfieldOf<E, S>.

Typedefs
using	BSC = SDMC<Fp<2>>
	Binary Symmetric Channel — type alias for SDMC<Fp<2>>.
template<class B>
using	base_t = std::remove_cvref_t<B>
template<class C>
using	field_t = typename base_t<C>::FIELD
template<uint16_t p, uint8_t m = 1>
using	label_t = typename std::conditional_t<sqm(p, m) < 255, uint8_t, uint16_t>

Enumerations
enum class	method_t {   BD , boosted_BD , ML , ML_soft ,   Viterbi , Viterbi_soft , BCJR , recursive ,   Meggitt , WBA , BMA , WBA_EE ,   BMA_EE , BD_EE , ML_EE , Viterbi_EE ,   recursive_EE }
enum class	LutMode { CompileTime , RunTime }
	LUT generation mode for field operations. More...

Functions
template<class LHS, class RHS>
decltype(auto)	operator>> (LHS &&lhs, RHS &&rhs)
	Function-call chaining: x >> f ≡ f(x).
template<class LHS, class RHS>
RHS &	operator>> (LHS &&lhs, RHS &dst)
	Assignment chaining: x >> dst ≡ dst = x; return dst.
template<FiniteFieldType T>
long double	HammingUpperBound (size_t n, size_t dmin)
template<FiniteFieldType T>
long double	JohnsonUpperBound (size_t n, size_t dmin)
template<FiniteFieldType T>
long double	PlotkinUpperBound (size_t n, size_t dmin)
template<FiniteFieldType T>
long double	EliasUpperBound (size_t n, size_t dmin)
size_t	SingletonUpperBound (size_t n, size_t dmin)
template<FiniteFieldType T>
size_t	GriesmerUpperBound (size_t n, size_t dmin)
template<FiniteFieldType T>
long double	UpperBound (size_t n, size_t dmin)
template<FiniteFieldType T>
size_t	GilbertVarshamovLowerBound (size_t n, size_t dmin)
template<FiniteFieldType T>
size_t	BurstUpperBound (size_t n, size_t ell)
size_t	ReigerBurstUpperBound (size_t n, size_t ell)
template<FiniteFieldType T>
Polynomial< InfInt >	MacWilliamsIdentity (const Polynomial< InfInt > &A, size_t n, size_t k)
std::ostream &	showbasic (std::ostream &os)
std::ostream &	showmost (std::ostream &os)
std::ostream &	showall (std::ostream &os)
std::ostream &	showspecial (std::ostream &os)
template<class B>
	SubfieldSubcode (const B &) -> SubfieldSubcode< B >
template<class B>
	SubfieldSubcode (B &&) -> SubfieldSubcode< B >
template<FieldType T>
auto	dual (const T &C)
template<class B>
auto	extend (B &&base, size_t i, const Vector< field_t< B > > &v)
template<class B>
auto	extend (B &&base)
template<FieldType T, class B>
B	unextend (const ExtendedCode< T, B > &C)
template<class B>
auto	augment (B &&base, size_t j, const Vector< field_t< B > > &w)
template<FieldType T, class B>
B	unaugment (const AugmentedCode< T, B > &C)
template<class B>
auto	lengthen (B &&base, size_t j, const Vector< field_t< B > > &w, size_t i, const Vector< field_t< B > > &v)
template<class B>
auto	lengthen (B &&base, size_t j, const Vector< field_t< B > > &w)
template<FieldType T, class D>
auto	unlengthen (const ExtendedCode< T, AugmentedCode< T, D > > &C)
template<FieldType T>
LinearCode< T >	puncture (const LinearCode< T > &C, const std::vector< size_t > &v)
template<FieldType T>
auto	puncture (const EmptyCode< T > &C, const std::vector< size_t > &v)
template<FieldType T>
auto	puncture (const ZeroCode< T > &C, const std::vector< size_t > &v)
template<FieldType T>
auto	puncture (const UniverseCode< T > &C, const std::vector< size_t > &v)
template<FieldType T>
auto	puncture (const RepetitionCode< T > &C, const std::vector< size_t > &v)
template<class C>
auto	puncture (C &&code, size_t i)
template<FieldType T>
LinearCode< T >	expurgate (const LinearCode< T > &C, const std::vector< size_t > &v)
template<FieldType T>
auto	expurgate (const EmptyCode< T > &C, const std::vector< size_t > &v)
template<FieldType T>
auto	expurgate (const ZeroCode< T > &C, const std::vector< size_t > &v)
template<FieldType T>
auto	expurgate (const RepetitionCode< T > &C, const std::vector< size_t > &v)
template<class C>
auto	expurgate (C &&code, size_t j)
template<class B>
auto	shorten (B &&base, size_t j, size_t i)
template<FieldType L, FieldType R>
bool	operator== (const LinearCode< L > &lhs, const LinearCode< R > &rhs)
template<FieldType L, FieldType R>
bool	operator!= (const LinearCode< L > &lhs, const LinearCode< R > &rhs)
template<FieldType L, FieldType R>
bool	identical (const LinearCode< L > &lhs, const LinearCode< R > &rhs)
template<FieldType L, FieldType R>
bool	equivalent (const LinearCode< L > &lhs, const LinearCode< R > &rhs)
template<FieldType T>
std::ostream &	operator<< (std::ostream &os, const Code< T > &rhs)
template<SignedIntType T>
std::ostream &	operator<< (std::ostream &os, const Rationals< T > &e)
	Print as "numerator/denominator" (or just "numerator" when denominator is 1).
template<uint16_t p>
std::ostream &	operator<< (std::ostream &os, const Fp< p > &e)
	Print as the integer label (or ERASURE_MARKER if erased).
template<FiniteFieldType B, MOD modulus, LutMode mode>
std::ostream &	operator<< (std::ostream &os, const Ext< B, modulus, mode > &e)
	Print as the integer label (or ERASURE_MARKER if erased).
std::mt19937 &	gen ()
	Current thread's random number generator.
template<class T>
std::vector< size_t >	find_maxima (const std::vector< T > &v)
	Indices of all maximum elements.
template<class T>
constexpr bool	is_prime (T a) noexcept
	Primality test by trial division.
template<class T>
constexpr T	GCD (T a, T b, T *s=nullptr, T *t=nullptr) noexcept
	Greatest common divisor and optional Bézout coefficients.
template<uint16_t p, class T>
constexpr T	modinv (T a) noexcept
	Multiplicative inverse modulo a prime.
template<class T>
T	fac (T a) noexcept
	Factorial a!
template<class T>
T	bin (const T &n, T k) noexcept
	Binomial coefficient C(n,k).
template<>
InfInt	bin (const InfInt &n, InfInt k) noexcept
	Binomial coefficient specialization for InfInt.
template<class T>
constexpr T	sqm (T b, int e)
	Exponentiation by square-and-multiply.
template<class T>
constexpr T	daa (T b, int m)
	Scalar multiplication by double-and-add.
template<ComponentType T>
constexpr Matrix< T >	ZeroMatrix (size_t m, size_t n)
	m × n matrix of zeros (tag details::Zero)
template<ComponentType T>
constexpr Matrix< T >	IdentityMatrix (size_t m)
	m × m identity matrix I_m (tag details::Identity)
template<ComponentType T>
constexpr Matrix< T >	DiagonalMatrix (const Vector< T > &v)
	Diagonal matrix with diagonal v (tag details::Diagonal).
template<ComponentType T>
constexpr Matrix< T >	ToeplitzMatrix (const Vector< T > &v, size_t m, size_t n)
	m × n Toeplitz matrix from its diagonal entries (tag details::Toeplitz)
template<ComponentType T>
constexpr Matrix< T >	VandermondeMatrix (const Vector< T > &v, size_t m)
	Vandermonde matrix V_{i, j} = v[j]^i (tag details::Vandermonde).
template<ComponentType T>
std::ostream &	operator<< (std::ostream &os, const Matrix< T > &rhs)
	Pretty-print the matrix with column alignment and bracket borders.
template<ComponentType T>
constexpr Matrix< T >	operator+ (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator+ (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator+ (const Matrix< T > &lhs, Matrix< T > &&rhs)
template<ComponentType T>
constexpr Matrix< T >	operator+ (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
constexpr Matrix< T >	operator- (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator- (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator- (const Matrix< T > &lhs, Matrix< T > &&rhs)
template<ComponentType T>
constexpr Matrix< T >	operator- (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
constexpr Matrix< T >	operator* (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator* (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator* (const Vector< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator* (Vector< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator* (const Matrix< T > &lhs, const T &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator* (Matrix< T > &&lhs, const T &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator* (const T &lhs, const Matrix< T > &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator* (const T &lhs, Matrix< T > &&rhs)
template<ComponentType T>
constexpr Matrix< T >	operator/ (const Matrix< T > &lhs, const T &rhs)
template<ComponentType T>
constexpr Matrix< T >	operator/ (Matrix< T > &&lhs, const T &rhs)
template<ComponentType T>
Matrix< T >	randomize (const Matrix< T > &M)
template<ComponentType T>
Matrix< T >	randomize (Matrix< T > &&M)
template<ReliablyComparableType T>
constexpr size_t	wH (const Matrix< T > &M)
template<ComponentType T> requires std::convertible_to<std::decay_t<decltype(M)>, Matrix<T>>
Matrix< T >	set_component (auto &&M, size_t i, size_t j, const T &c)
template<ComponentType T>
Matrix< T >	get_submatrix (const Matrix< T > &M, size_t i, size_t j, size_t h, size_t w)
template<ComponentType T>
Matrix< T >	get_submatrix (Matrix< T > &&M, size_t i, size_t j, size_t h, size_t w)
template<ComponentType T>
Matrix< T >	set_submatrix (const Matrix< T > &M, size_t i, size_t j, const Matrix< T > &N)
template<ComponentType T>
Matrix< T >	set_submatrix (Matrix< T > &&M, size_t i, size_t j, const Matrix< T > &N)
template<ComponentType T>
Matrix< T >	horizontal_join (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	horizontal_join (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	horizontal_join (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
Matrix< T >	vertical_join (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	vertical_join (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	vertical_join (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
Matrix< T >	diagonal_join (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	diagonal_join (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	diagonal_join (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
Matrix< T >	Kronecker_product (const Matrix< T > &lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	Kronecker_product (Matrix< T > &&lhs, const Matrix< T > &rhs)
template<ComponentType T>
Matrix< T >	Kronecker_product (Matrix< T > &&lhs, Matrix< T > &&rhs)
template<ComponentType T>
Matrix< T >	swap_rows (const Matrix< T > &M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	swap_columns (const Matrix< T > &M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	swap_rows (Matrix< T > &&M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	swap_columns (Matrix< T > &&M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	scale_row (const Matrix< T > &M, const T &s, size_t i)
template<ComponentType T>
Matrix< T >	scale_column (const Matrix< T > &M, const T &s, size_t i)
template<ComponentType T>
Matrix< T >	scale_row (Matrix< T > &&M, const T &s, size_t i)
template<ComponentType T>
Matrix< T >	scale_column (Matrix< T > &&M, const T &s, size_t i)
template<ComponentType T>
Matrix< T >	add_scaled_row (const Matrix< T > &M, const T &s, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_scaled_column (const Matrix< T > &M, const T &s, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_scaled_row (Matrix< T > &&M, const T &s, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_scaled_column (Matrix< T > &&M, const T &s, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_row (const Matrix< T > &M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_column (const Matrix< T > &M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_row (Matrix< T > &&M, size_t i, size_t j)
template<ComponentType T>
Matrix< T >	add_column (Matrix< T > &&M, size_t i, size_t j)
template<ComponentType T>
constexpr Matrix< T >	delete_columns (const Matrix< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	delete_columns (Matrix< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	delete_column (const Matrix< T > &lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	delete_column (Matrix< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	delete_rows (const Matrix< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	delete_rows (Matrix< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	delete_row (const Matrix< T > &lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	delete_row (Matrix< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	erase_component (const Matrix< T > &lhs, size_t i, size_t j)
template<ComponentType T>
constexpr Matrix< T >	erase_component (Matrix< T > &&lhs, size_t i, size_t j)
template<ComponentType T>
constexpr Matrix< T >	unerase_component (const Matrix< T > &lhs, size_t i, size_t j)
template<ComponentType T>
constexpr Matrix< T >	unerase_component (Matrix< T > &&lhs, size_t i, size_t j)
template<ComponentType T>
constexpr Matrix< T >	erase_columns (const Matrix< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	erase_columns (Matrix< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	erase_column (const Matrix< T > &lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	erase_column (Matrix< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	unerase_columns (const Matrix< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	unerase_columns (Matrix< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	unerase_column (const Matrix< T > &lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	unerase_column (Matrix< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	erase_rows (const Matrix< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	erase_rows (Matrix< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	erase_row (const Matrix< T > &lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	erase_row (Matrix< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	unerase_rows (const Matrix< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	unerase_rows (Matrix< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
constexpr Matrix< T >	unerase_row (const Matrix< T > &lhs, size_t i)
template<ComponentType T>
constexpr Matrix< T >	unerase_row (Matrix< T > &&lhs, size_t i)
template<ComponentType T>
Matrix< T >	reverse_rows (const Matrix< T > &M)
template<ComponentType T>
Matrix< T >	reverse_rows (Matrix< T > &&M)
template<ComponentType T>
Matrix< T >	reverse_columns (const Matrix< T > &M)
template<ComponentType T>
Matrix< T >	reverse_columns (Matrix< T > &&M)
template<ComponentType T>
constexpr Matrix< T >	fill (const Matrix< T > &m, const T &value)
template<ComponentType T>
constexpr Matrix< T >	fill (Matrix< T > &&m, const T &value)
template<ComponentType T>
constexpr Matrix< T >	transpose (const Matrix< T > &M)
template<ComponentType T>
constexpr Matrix< T >	transpose (Matrix< T > &&M)
template<FieldType T>
Matrix< T >	rref (const Matrix< T > &M)
template<FieldType T>
Matrix< T >	rref (Matrix< T > &&M)
template<ComponentType T>
Matrix< T >	inverse (const Matrix< T > &M)
template<ComponentType T>
Matrix< T >	inverse (Matrix< T > &&M)
template<ReliablyComparableType T>
constexpr bool	operator== (const Matrix< T > &lhs, const Matrix< T > &rhs)
	Equality of two matrices.
template<ReliablyComparableType T>
constexpr bool	operator!= (const Matrix< T > &lhs, const Matrix< T > &rhs)
	Negation of operator==.
template<ComponentType T>
constexpr Matrix< T >	PermutationMatrix (const std::vector< size_t > &perm)
	Permutation matrix P with P_{i, perm[i]} = 1.
template<ComponentType T>
constexpr Matrix< T >	ExchangeMatrix (size_t m)
	m × m exchange matrix (ones on the anti-diagonal)
template<ComponentType T>
constexpr Matrix< T >	HankelMatrix (const Vector< T > &v, size_t m, size_t n)
	m × n Hankel matrix from its anti-diagonal entries
template<ComponentType T>
constexpr Matrix< T >	UpperShiftMatrix (size_t m)
	m × m upper shift matrix (ones on the superdiagonal)
template<ComponentType T>
constexpr Matrix< T >	LowerShiftMatrix (size_t m)
	m × m lower shift matrix (ones on the subdiagonal); transpose of UpperShiftMatrix
template<ComponentType T>
constexpr Matrix< T >	CompanionMatrix (const Polynomial< T > &poly)
	Companion matrix of a monic polynomial p(x) = x^n + a_{n−1} x^{n−1} + … + a_0.
template<ComponentType T>
constexpr bool	operator== (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<ComponentType T>
std::ostream &	operator<< (std::ostream &os, const Polynomial< T > &rhs)
template<ComponentType T>
Polynomial< T >	ZeroPolynomial ()
	Constant polynomial 0 (cached).
template<ComponentType T>
constexpr Polynomial< T >	operator+ (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator+ (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator+ (const Polynomial< T > &lhs, Polynomial< T > &&rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator+ (Polynomial< T > &&lhs, Polynomial< T > &&rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator- (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator- (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator- (const Polynomial< T > &lhs, Polynomial< T > &&rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator- (Polynomial< T > &&lhs, Polynomial< T > &&rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator* (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator* (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator* (const Polynomial< T > &lhs, Polynomial< T > &&rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator* (Polynomial< T > &&lhs, Polynomial< T > &&rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator/ (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator/ (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator% (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator% (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator* (const Polynomial< T > &lhs, const T &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator* (Polynomial< T > &&lhs, const T &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator* (const T &lhs, const Polynomial< T > &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator* (const T &lhs, Polynomial< T > &&rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator/ (const Polynomial< T > &lhs, const T &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator/ (Polynomial< T > &&lhs, const T &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator* (const Polynomial< T > &lhs, size_t n)
template<ComponentType T>
constexpr Polynomial< T >	operator* (Polynomial< T > &&lhs, size_t n)
template<ComponentType T>
constexpr Polynomial< T >	operator* (size_t n, const Polynomial< T > &rhs)
template<ComponentType T>
constexpr Polynomial< T >	operator* (size_t n, Polynomial< T > &&rhs)
template<ComponentType T>
std::pair< Polynomial< T >, Polynomial< T > >	poly_long_div (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<ComponentType T>
std::pair< Polynomial< T >, Polynomial< T > >	poly_long_div (Polynomial< T > &&lhs, const Polynomial< T > &rhs)
template<ComponentType T> requires FieldType<T>
constexpr Polynomial< T >	derivative (const Polynomial< T > &poly, size_t s)
template<ComponentType T> requires FieldType<T>
constexpr Polynomial< T >	derivative (Polynomial< T > &&poly, size_t s)
template<ComponentType T> requires FieldType<T>
constexpr Polynomial< T >	Hasse_derivative (const Polynomial< T > &poly, size_t s)
template<ComponentType T> requires FieldType<T>
constexpr Polynomial< T >	Hasse_derivative (Polynomial< T > &&poly, size_t s)
template<ComponentType T>
constexpr Polynomial< T >	reciprocal (const Polynomial< T > &poly)
template<ComponentType T>
constexpr Polynomial< T >	reciprocal (Polynomial< T > &&poly)
template<ComponentType T> requires FieldType<T>
constexpr Polynomial< T >	normalize (const Polynomial< T > &poly)
template<ComponentType T> requires FieldType<T>
constexpr Polynomial< T >	normalize (Polynomial< T > &&poly)
template<ComponentType T>
constexpr bool	operator!= (const Polynomial< T > &lhs, const Polynomial< T > &rhs)
template<ComponentType T> requires std::convertible_to<std::decay_t<decltype(a)>, T>
constexpr Polynomial< T >	Monomial (size_t i, auto &&a=T(1))
	Monomial a · xⁱ
template<ComponentType T>
Polynomial< T >	OnePolynomial ()
	Constant polynomial 1 (cached).
template<ComponentType T> requires FieldType<T>
Polynomial< T >	GCD (Polynomial< T > a, Polynomial< T > b, Polynomial< T > *s=nullptr, Polynomial< T > *t=nullptr)
	Greatest common divisor of two polynomials via the (extended) Euclidean algorithm.
template<ComponentType T> requires FieldType<T>
Polynomial< T >	GCD (const std::vector< Polynomial< T > > &polys)
	Greatest common divisor of a list of polynomials, computed iteratively.
template<ComponentType T> requires FieldType<T>
Polynomial< T >	LCM (const Polynomial< T > &a, const Polynomial< T > &b)
	Least common multiple lcm(a, b) = (a · b) / gcd(a, b).
template<ComponentType T> requires FieldType<T>
Polynomial< T >	LCM (const std::vector< Polynomial< T > > &polys)
	Least common multiple of a list of polynomials, computed iteratively.
template<ComponentType T>
constexpr Polynomial< T >	operator^ (const Polynomial< T > &base, int exponent)
	Polynomial exponentiation by square-and-multiply.
template<uint16_t p, size_t m>
constexpr Vector< Fp< p > >	ConwayCoefficients ()
	Coefficient vector [a₀, a₁, …, aₘ] of the Conway polynomial for 𝔽_{p^m}.
template<uint16_t p, size_t m>
constexpr Polynomial< Fp< p > >	ConwayPolynomial ()
	Conway polynomial for 𝔽_{p^m} as a Polynomial<Fp<p>>.
template<FieldType T>
Polynomial< T >	find_irreducible (size_t degree)
	Sample a random monic irreducible polynomial of degree degree over T.
template<FieldType T>
std::ostream &	operator<< (std::ostream &os, const Trellis< T > &Tr)
template<ComponentType T>
T	inner_product (const Vector< T > &lhs, const Vector< T > &rhs)
	Inner product ⟨lhs, rhs⟩ = Σᵢ lhs[i] · rhs[i].
template<ComponentType T>
Vector< T >	Schur_product (const Vector< T > &lhs, const Vector< T > &rhs)
	Schur (component-wise) product.
template<ComponentType T>
Vector< T >	unit_vector (size_t length, size_t i)
	Length-length vector with T(1) at index i and zeros elsewhere.
template<ComponentType T>
std::ostream &	operator<< (std::ostream &os, const Vector< T > &rhs)
	Stream output as ( c₀, c₁, …, cₙ₋₁ ).
template<ComponentType T>
Vector< T >	delete_component (const Vector< T > &lhs, size_t i)
template<ComponentType T>
Vector< T >	delete_component (Vector< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Vector< T >	operator+ (const Vector< T > &lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator+ (Vector< T > &&lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator+ (const Vector< T > &lhs, Vector< T > &&rhs)
template<ComponentType T>
constexpr Vector< T >	operator+ (Vector< T > &&lhs, Vector< T > &&rhs)
template<ComponentType T>
constexpr Vector< T >	operator- (const Vector< T > &lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator- (Vector< T > &&lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	operator- (const Vector< T > &lhs, Vector< T > &&rhs)
template<ComponentType T>
constexpr Vector< T >	operator- (Vector< T > &&lhs, Vector< T > &&rhs)
template<ComponentType T>
constexpr Vector< T >	operator* (const Vector< T > &lhs, const T &rhs) noexcept
template<ComponentType T>
constexpr Vector< T >	operator* (Vector< T > &&lhs, const T &rhs) noexcept
template<ComponentType T>
constexpr Vector< T >	operator* (const T &lhs, const Vector< T > &rhs) noexcept
template<ComponentType T>
constexpr Vector< T >	operator* (const T &lhs, Vector< T > &&rhs) noexcept
template<ComponentType T>
constexpr Vector< T >	operator/ (const Vector< T > &lhs, const T &rhs)
template<FieldType T>
constexpr Vector< T >	operator/ (Vector< T > &&lhs, const T &rhs)
template<ComponentType T>
Vector< T >	convolve (const Vector< T > &v, const Vector< T > &w)
	Discrete linear convolution (= coefficients of Polynomial(v) * Polynomial(w)).
template<ComponentType T>
Vector< T >	randomize (const Vector< T > &v)
template<ComponentType T>
Vector< T >	randomize (Vector< T > &&v)
template<ComponentType T>
Vector< T >	set_component (const Vector< T > &v, size_t i, const T &c)
template<ComponentType T>
Vector< T >	set_component (Vector< T > &&v, size_t i, const T &c)
template<ComponentType T>
constexpr Vector< T >	get_subvector (const Vector< T > &v, size_t start, size_t end)
template<ComponentType T>
constexpr Vector< T >	get_subvector (Vector< T > &&v, size_t start, size_t end)
template<ComponentType T>
constexpr Vector< T >	set_subvector (Vector< T > v, size_t start, const Vector< T > &w)
template<ComponentType T>
constexpr Vector< T >	set_subvector (Vector< T > &&v, size_t start, const Vector< T > &w)
template<ComponentType T>
constexpr Vector< T >	concatenate (const Vector< T > &lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	concatenate (Vector< T > &&lhs, const Vector< T > &rhs)
template<ComponentType T>
constexpr Vector< T >	concatenate (const Vector< T > &lhs, Vector< T > &&rhs)
template<ComponentType T>
constexpr Vector< T >	concatenate (Vector< T > &&lhs, Vector< T > &&rhs)
template<ComponentType T>
Vector< T >	delete_components (const Vector< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
Vector< T >	delete_components (Vector< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
Vector< T >	erase_components (const Vector< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
Vector< T >	erase_components (Vector< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
Vector< T >	erase_component (const Vector< T > &lhs, size_t i)
template<ComponentType T>
Vector< T >	erase_component (Vector< T > &&lhs, size_t i)
template<ComponentType T>
Vector< T >	unerase_components (const Vector< T > &lhs, const std::vector< size_t > &v)
template<ComponentType T>
Vector< T >	unerase_components (Vector< T > &&lhs, const std::vector< size_t > &v)
template<ComponentType T>
Vector< T >	unerase_component (const Vector< T > &lhs, size_t i)
template<ComponentType T>
Vector< T >	unerase_component (Vector< T > &&lhs, size_t i)
template<ComponentType T>
constexpr Vector< T >	pad_front (const Vector< T > &v, size_t n)
template<ComponentType T>
constexpr Vector< T >	pad_front (Vector< T > &&v, size_t n)
template<ComponentType T>
constexpr Vector< T >	pad_back (const Vector< T > &v, size_t n)
template<ComponentType T>
constexpr Vector< T >	pad_back (Vector< T > &&v, size_t n)
template<ComponentType T>
constexpr Vector< T >	rotate_left (const Vector< T > &v, size_t i)
template<ComponentType T>
constexpr Vector< T >	rotate_left (Vector< T > &&v, size_t i)
template<ComponentType T>
constexpr Vector< T >	rotate_right (const Vector< T > &v, size_t i)
template<ComponentType T>
constexpr Vector< T >	rotate_right (Vector< T > &&v, size_t i)
template<ComponentType T>
constexpr Vector< T >	reverse (const Vector< T > &v)
template<ComponentType T>
constexpr Vector< T >	reverse (Vector< T > &&v)
template<ComponentType T>
constexpr Vector< T >	fill (const Vector< T > &v, const T &value)
template<ComponentType T>
constexpr Vector< T >	fill (Vector< T > &&v, const T &value)
template<ReliablyComparableType T>
constexpr bool	operator== (const Vector< T > &lhs, const Vector< T > &rhs) noexcept
template<ReliablyComparableType T>
constexpr bool	operator!= (const Vector< T > &lhs, const Vector< T > &rhs) noexcept
Field Arithmetic Operators
Free CRTP operators (+, −, *, /, ^) for any CECCO::FieldType Each operator constructs a result by calling T's compound assignment, with rvalue overloads that move from a temporary instead of copying. Scalar multiplication takes the integer on either side. Division throws std::invalid_argument if the right operand is zero. operator^ exponentiates by square-and-multiply via CECCO::sqm. Warning operator^ does not follow C++ precedence for ^: in b * a ^ p the parser evaluates (b * a) ^ p. Parenthesise as b * (a ^ p), or call CECCO::sqm directly.
template<FieldType T>
constexpr T	operator+ (const T &lhs, const T &rhs)
template<FieldType T>
constexpr T	operator+ (T &&lhs, const T &rhs)
template<FieldType T>
constexpr T	operator+ (const T &lhs, T &&rhs)
template<FieldType T>
constexpr T	operator+ (T &&lhs, T &&rhs)
template<FieldType T>
constexpr T	operator- (const T &lhs, const T &rhs)
template<FieldType T>
constexpr T	operator- (T &&lhs, const T &rhs)
template<FieldType T>
constexpr T	operator- (const T &lhs, T &&rhs)
template<FieldType T>
constexpr T	operator- (T &&lhs, T &&rhs)
template<FieldType T>
constexpr T	operator* (const T &lhs, const T &rhs)
template<FieldType T>
constexpr T	operator* (T &&lhs, const T &rhs)
template<FieldType T>
constexpr T	operator* (const T &lhs, T &&rhs)
template<FieldType T>
constexpr T	operator* (T &&lhs, T &&rhs)
template<FieldType T>
constexpr T	operator* (const T &lhs, uint16_t rhs)
template<FieldType T>
constexpr T	operator* (uint16_t lhs, const T &rhs)
template<FieldType T>
constexpr T	operator* (T &&lhs, int rhs)
template<FieldType T>
constexpr T	operator* (int lhs, T &&rhs)
template<FieldType T>
T	operator/ (const T &lhs, const T &rhs)
template<FieldType T>
T	operator/ (T &&lhs, const T &rhs)
template<FieldType T>
constexpr T	operator^ (const T &base, int exponent)
template<FieldType T>
constexpr T	operator^ (T &&base, int exponent)
Error control coding-related functions
double	dE (const Vector< std::complex< double > > &lhs, const Vector< std::complex< double > > &rhs)
	Euclidean distance ‖lhs − rhs‖₂ = √(Σᵢ |lhs[i] − rhs[i]|²) for complex vectors.
template<ReliablyComparableType T>
constexpr size_t	wH (const Vector< T > &v) noexcept
	Hamming weight; see Vector::wH for semantics.
template<ReliablyComparableType T>
std::vector< size_t >	supp (const Vector< T > &v)
	Support; see Vector::supp for semantics.
template<ReliablyComparableType T>
size_t	dH (const Vector< T > &lhs, const Vector< T > &rhs)
	Hamming distance dₕ(lhs, rhs) = wₕ(lhs − rhs).
template<ReliablyComparableType T>
size_t	dH (Vector< T > &&lhs, const Vector< T > &rhs)
template<ReliablyComparableType T>
size_t	dH (const Vector< T > &lhs, Vector< T > &&rhs)
template<ReliablyComparableType T>
size_t	dH (Vector< T > &&lhs, Vector< T > &&rhs)
template<ReliablyComparableType T>
constexpr size_t	burst_length (const Vector< T > &v) noexcept
	Burst length; see Vector::burst_length for semantics.
template<ReliablyComparableType T>
constexpr size_t	cyclic_burst_length (const Vector< T > &v) noexcept
	Cyclic burst length; see Vector::cyclic_burst_length for semantics.

Variables
constexpr std::string_view	ERASURE_MARKER = "X"

Detailed Description

Provides a framework for error correcting codes.

Typedef Documentation

base_t

template<class B>

using CECCO::base_t = std::remove_cvref_t<B>

Definition at line 4509 of file codes.hpp.

BSC

using CECCO::BSC = SDMC<Fp<2>>

Binary Symmetric Channel — type alias for SDMC<Fp<2>>.

Bits are flipped with probability pe.

See also

CECCO::SDMC, CECCO::BEC

Definition at line 370 of file blocks.hpp.

field_t

template<class C>

using CECCO::field_t = typename base_t<C>::FIELD

Definition at line 4512 of file codes.hpp.

label_t

template<uint16_t p, uint8_t m = 1>

using CECCO::label_t = typename std::conditional_t<sqm(p, m) < 255, uint8_t, uint16_t>

Definition at line 774 of file fields.hpp.

Enumeration Type Documentation

LutMode

enum class CECCO::LutMode

strong

LUT generation mode for field operations.

Enumerator
CompileTime	Generate LUTs at compile-time using constexpr (default).
RunTime	Generate LUTs at runtime using lazy initialization.

Definition at line 53 of file field_concepts_traits.hpp.

method_t

enum class CECCO::method_t

strong

Enumerator
BD
boosted_BD
ML
ML_soft
Viterbi
Viterbi_soft
BCJR
recursive
Meggitt
WBA
BMA
WBA_EE
BMA_EE
BD_EE
ML_EE
Viterbi_EE
recursive_EE

Definition at line 4688 of file codes.hpp.

Function Documentation

add_column() [1/2]

template<ComponentType T>

Matrix< T > CECCO::add_column	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j )

Definition at line 3017 of file matrices.hpp.

add_column() [2/2]

template<ComponentType T>

Matrix< T > CECCO::add_column	(	Matrix< T > &&	M,
		size_t	i,
		size_t	j )

Definition at line 3031 of file matrices.hpp.

add_row() [1/2]

template<ComponentType T>

Matrix< T > CECCO::add_row	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j )

Definition at line 3010 of file matrices.hpp.

add_row() [2/2]

template<ComponentType T>

Matrix< T > CECCO::add_row	(	Matrix< T > &&	M,
		size_t	i,
		size_t	j )

Definition at line 3024 of file matrices.hpp.

add_scaled_column() [1/2]

template<ComponentType T>

Matrix< T > CECCO::add_scaled_column	(	const Matrix< T > &	M,
		const T &	s,
		size_t	i,
		size_t	j )

Definition at line 2989 of file matrices.hpp.

add_scaled_column() [2/2]

template<ComponentType T>

Matrix< T > CECCO::add_scaled_column	(	Matrix< T > &&	M,
		const T &	s,
		size_t	i,
		size_t	j )

Definition at line 3003 of file matrices.hpp.

add_scaled_row() [1/2]

template<ComponentType T>

Matrix< T > CECCO::add_scaled_row	(	const Matrix< T > &	M,
		const T &	s,
		size_t	i,
		size_t	j )

Definition at line 2982 of file matrices.hpp.

add_scaled_row() [2/2]

template<ComponentType T>

Matrix< T > CECCO::add_scaled_row	(	Matrix< T > &&	M,
		const T &	s,
		size_t	i,
		size_t	j )

Definition at line 2996 of file matrices.hpp.

augment()

template<class B>

auto CECCO::augment	(	B &&	base,
		size_t	j,
		const Vector< field_t< B > > &	w )

Definition at line 4535 of file codes.hpp.

bin() [1/2]

template<>

InfInt CECCO::bin ( const InfInt & n, InfInt k )

inlinenoexcept

Binomial coefficient specialization for InfInt.

Parameters

n	Total number of items
k	Number of items to choose

Returns

C(n,k) as an InfInt

Builds numerator and denominator separately, then performs one division.

Definition at line 271 of file helpers.hpp.

Here is the call graph for this function:

bin() [2/2]

template<class T>

T CECCO::bin ( const T & n, T k )

noexcept

Binomial coefficient C(n,k).

Template Parameters

T	Integer type

Parameters

n	Total number of items
k	Number of items to choose

Returns

C(n,k) = n! / (k! * (n-k)!)

Uses the multiplicative formula and the symmetry C(n,k) = C(n,n-k).

Definition at line 253 of file helpers.hpp.

burst_length()

template<ReliablyComparableType T>

size_t CECCO::burst_length ( const Vector< T > & v )

constexprnoexcept

Burst length; see Vector::burst_length for semantics.

Definition at line 1637 of file vectors.hpp.

BurstUpperBound()

template<FiniteFieldType T>

size_t CECCO::BurstUpperBound	(	size_t	n,
		size_t	ell )

Definition at line 236 of file code_bounds.hpp.

CompanionMatrix()

template<ComponentType T>

Matrix< T > CECCO::CompanionMatrix ( const Polynomial< T > & poly )

constexpr

Companion matrix of a monic polynomial p(x) = x^n + a_{n−1} x^{n−1} + … + a_0.

Parameters

poly	Monic polynomial of degree n

Returns

n × n matrix whose characteristic polynomial is poly

Built from a lower shift matrix; the last column holds the negated coefficients of poly.

Exceptions

std::invalid_argument

if poly is not monic

Definition at line 3641 of file matrices.hpp.

concatenate() [1/4]

template<ComponentType T>

Vector< T > CECCO::concatenate ( const Vector< T > & lhs, const Vector< T > & rhs )

constexpr

Definition at line 1320 of file vectors.hpp.

concatenate() [2/4]

template<ComponentType T>

Vector< T > CECCO::concatenate ( const Vector< T > & lhs, Vector< T > && rhs )

constexpr

Definition at line 1334 of file vectors.hpp.

concatenate() [3/4]

template<ComponentType T>

Vector< T > CECCO::concatenate ( Vector< T > && lhs, const Vector< T > & rhs )

constexpr

Definition at line 1327 of file vectors.hpp.

concatenate() [4/4]

template<ComponentType T>

Vector< T > CECCO::concatenate ( Vector< T > && lhs, Vector< T > && rhs )

constexpr

Definition at line 1341 of file vectors.hpp.

convolve()

template<ComponentType T>

Vector< T > CECCO::convolve	(	const Vector< T > &	v,
		const Vector< T > &	w )

Discrete linear convolution (= coefficients of Polynomial(v) * Polynomial(w)).

Definition at line 1267 of file vectors.hpp.

ConwayCoefficients()

template<uint16_t p, size_t m>

Vector< Fp< p > > CECCO::ConwayCoefficients ( )

constexpr

Coefficient vector [a₀, a₁, …, aₘ] of the Conway polynomial for 𝔽_{p^m}.

Template Parameters

p	Prime characteristic
m	Extension degree

Returns

Coefficients low-to-high; empty vector if the (p, m) pair is not in the built-in table

The built-in table covers all primes ≤ 97 and degrees ≤ ~13 (more for small p).

Definition at line 1408 of file polynomials.hpp.

ConwayPolynomial()

template<uint16_t p, size_t m>

Polynomial< Fp< p > > CECCO::ConwayPolynomial ( )

constexpr

Conway polynomial for 𝔽_{p^m} as a Polynomial<Fp<p>>.

Wraps ConwayCoefficients; returns the empty polynomial if (p, m) is not tabulated.

Definition at line 1594 of file polynomials.hpp.

cyclic_burst_length()

template<ReliablyComparableType T>

size_t CECCO::cyclic_burst_length ( const Vector< T > & v )

constexprnoexcept

Cyclic burst length; see Vector::cyclic_burst_length for semantics.

Definition at line 1643 of file vectors.hpp.

daa()

template<class T>

T CECCO::daa ( T b, int m )

constexpr

Scalar multiplication by double-and-add.

Template Parameters

T	Type supporting addition and unary minus

Parameters

b	Multiplicand
m	Integer multiplier

Returns

b * m

For negative multipliers, computes (-b) * |m|.

Note

Returns T(0) for m = 0.

Definition at line 330 of file helpers.hpp.

dE()

double CECCO::dE ( const Vector< std::complex< double > > & lhs, const Vector< std::complex< double > > & rhs )

inline

Euclidean distance ‖lhs − rhs‖₂ = √(Σᵢ |lhs[i] − rhs[i]|²) for complex vectors.

Exceptions

std::invalid_argument

if lengths differ

Definition at line 1651 of file vectors.hpp.

delete_column() [1/2]

template<ComponentType T>

Matrix< T > CECCO::delete_column ( const Matrix< T > & lhs, size_t i )

constexpr

Definition at line 3052 of file matrices.hpp.

delete_column() [2/2]

template<ComponentType T>

Matrix< T > CECCO::delete_column ( Matrix< T > && lhs, size_t i )

constexpr

Definition at line 3059 of file matrices.hpp.

delete_columns() [1/2]

template<ComponentType T>

Matrix< T > CECCO::delete_columns ( const Matrix< T > & lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3038 of file matrices.hpp.

delete_columns() [2/2]

template<ComponentType T>

Matrix< T > CECCO::delete_columns ( Matrix< T > && lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3045 of file matrices.hpp.

delete_component() [1/2]

template<ComponentType T>

Vector< T > CECCO::delete_component	(	const Vector< T > &	lhs,
		size_t	i )

Definition at line 784 of file vectors.hpp.

delete_component() [2/2]

template<ComponentType T>

Vector< T > CECCO::delete_component	(	Vector< T > &&	lhs,
		size_t	i )

Definition at line 791 of file vectors.hpp.

delete_components() [1/2]

template<ComponentType T>

Vector< T > CECCO::delete_components	(	const Vector< T > &	lhs,
		const std::vector< size_t > &	v )

Definition at line 1348 of file vectors.hpp.

delete_components() [2/2]

template<ComponentType T>

Vector< T > CECCO::delete_components	(	Vector< T > &&	lhs,
		const std::vector< size_t > &	v )

Definition at line 1355 of file vectors.hpp.

delete_row() [1/2]

template<ComponentType T>

Matrix< T > CECCO::delete_row ( const Matrix< T > & lhs, size_t i )

constexpr

Definition at line 3080 of file matrices.hpp.

delete_row() [2/2]

template<ComponentType T>

Matrix< T > CECCO::delete_row ( Matrix< T > && lhs, size_t i )

constexpr

Definition at line 3087 of file matrices.hpp.

delete_rows() [1/2]

template<ComponentType T>

Matrix< T > CECCO::delete_rows ( const Matrix< T > & lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3066 of file matrices.hpp.

delete_rows() [2/2]

template<ComponentType T>

Matrix< T > CECCO::delete_rows ( Matrix< T > && lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3073 of file matrices.hpp.

derivative() [1/2]

template<ComponentType T>
requires FieldType<T>

Polynomial< T > CECCO::derivative ( const Polynomial< T > & poly, size_t s )

constexpr

Definition at line 1138 of file polynomials.hpp.

derivative() [2/2]

template<ComponentType T>
requires FieldType<T>

Polynomial< T > CECCO::derivative ( Polynomial< T > && poly, size_t s )

constexpr

Definition at line 1147 of file polynomials.hpp.

dH() [1/4]

template<ReliablyComparableType T>

size_t CECCO::dH	(	const Vector< T > &	lhs,
		const Vector< T > &	rhs )

Hamming distance dₕ(lhs, rhs) = wₕ(lhs − rhs).

Number of positions in which lhs and rhs differ. Under CECCO_ERASURE_SUPPORT, positions where either side is erased are not counted (subtraction propagates the erasure marker, and wH skips erased components).

Exceptions

std::invalid_argument

if lengths differ

Definition at line 1600 of file vectors.hpp.

dH() [2/4]

template<ReliablyComparableType T>

size_t CECCO::dH	(	const Vector< T > &	lhs,
		Vector< T > &&	rhs )

Definition at line 1619 of file vectors.hpp.

dH() [3/4]

template<ReliablyComparableType T>

size_t CECCO::dH	(	Vector< T > &&	lhs,
		const Vector< T > &	rhs )

Definition at line 1610 of file vectors.hpp.

dH() [4/4]

template<ReliablyComparableType T>

size_t CECCO::dH	(	Vector< T > &&	lhs,
		Vector< T > &&	rhs )

Definition at line 1627 of file vectors.hpp.

diagonal_join() [1/3]

template<ComponentType T>

Matrix< T > CECCO::diagonal_join	(	const Matrix< T > &	lhs,
		const Matrix< T > &	rhs )

Definition at line 2884 of file matrices.hpp.

diagonal_join() [2/3]

template<ComponentType T>

Matrix< T > CECCO::diagonal_join	(	Matrix< T > &&	lhs,
		const Matrix< T > &	rhs )

Definition at line 2891 of file matrices.hpp.

diagonal_join() [3/3]

template<ComponentType T>

Matrix< T > CECCO::diagonal_join	(	Matrix< T > &&	lhs,
		Matrix< T > &&	rhs )

Definition at line 2898 of file matrices.hpp.

DiagonalMatrix()

template<ComponentType T>

Matrix< T > CECCO::DiagonalMatrix ( const Vector< T > & v )

constexpr

Diagonal matrix with diagonal v (tag details::Diagonal).

Parameters

v	Vector of diagonal entries; the result is v.length() × v.length()

Returns

Diagonal matrix with v[i] on position (i, i), zeros elsewhere

Definition at line 3511 of file matrices.hpp.

dual()

template<FieldType T>

auto CECCO::dual

(

const T &

C

)

Definition at line 4493 of file codes.hpp.

EliasUpperBound()

template<FiniteFieldType T>

long double CECCO::EliasUpperBound	(	size_t	n,
		size_t	dmin )

Definition at line 127 of file code_bounds.hpp.

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equivalent()

template<FieldType L, FieldType R>

bool CECCO::equivalent	(	const LinearCode< L > &	lhs,
		const LinearCode< R > &	rhs )

Definition at line 4667 of file codes.hpp.

erase_column() [1/2]

template<ComponentType T>

Matrix< T > CECCO::erase_column ( const Matrix< T > & lhs, size_t i )

constexpr

Definition at line 3138 of file matrices.hpp.

erase_column() [2/2]

template<ComponentType T>

Matrix< T > CECCO::erase_column ( Matrix< T > && lhs, size_t i )

constexpr

Definition at line 3145 of file matrices.hpp.

erase_columns() [1/2]

template<ComponentType T>

Matrix< T > CECCO::erase_columns ( const Matrix< T > & lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3124 of file matrices.hpp.

erase_columns() [2/2]

template<ComponentType T>

Matrix< T > CECCO::erase_columns ( Matrix< T > && lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3131 of file matrices.hpp.

erase_component() [1/4]

template<ComponentType T>

Matrix< T > CECCO::erase_component ( const Matrix< T > & lhs, size_t i, size_t j )

constexpr

Definition at line 3096 of file matrices.hpp.

erase_component() [2/4]

template<ComponentType T>

Vector< T > CECCO::erase_component	(	const Vector< T > &	lhs,
		size_t	i )

Definition at line 1378 of file vectors.hpp.

erase_component() [3/4]

template<ComponentType T>

Matrix< T > CECCO::erase_component ( Matrix< T > && lhs, size_t i, size_t j )

constexpr

Definition at line 3103 of file matrices.hpp.

erase_component() [4/4]

template<ComponentType T>

Vector< T > CECCO::erase_component	(	Vector< T > &&	lhs,
		size_t	i )

Definition at line 1385 of file vectors.hpp.

erase_components() [1/2]

template<ComponentType T>

Vector< T > CECCO::erase_components	(	const Vector< T > &	lhs,
		const std::vector< size_t > &	v )

Definition at line 1364 of file vectors.hpp.

erase_components() [2/2]

template<ComponentType T>

Vector< T > CECCO::erase_components	(	Vector< T > &&	lhs,
		const std::vector< size_t > &	v )

Definition at line 1371 of file vectors.hpp.

erase_row() [1/2]

template<ComponentType T>

Matrix< T > CECCO::erase_row ( const Matrix< T > & lhs, size_t i )

constexpr

Definition at line 3194 of file matrices.hpp.

erase_row() [2/2]

template<ComponentType T>

Matrix< T > CECCO::erase_row ( Matrix< T > && lhs, size_t i )

constexpr

Definition at line 3201 of file matrices.hpp.

erase_rows() [1/2]

template<ComponentType T>

Matrix< T > CECCO::erase_rows ( const Matrix< T > & lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3180 of file matrices.hpp.

erase_rows() [2/2]

template<ComponentType T>

Matrix< T > CECCO::erase_rows ( Matrix< T > && lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3187 of file matrices.hpp.

ExchangeMatrix()

template<ComponentType T>

Matrix< T > CECCO::ExchangeMatrix ( size_t m )

constexpr

m × m exchange matrix (ones on the anti-diagonal)

Parameters

m	Side length

Returns

Matrix with E_{i, j} = 1 iff i + j = m − 1

Definition at line 3498 of file matrices.hpp.

expurgate() [1/5]

template<class C>

auto CECCO::expurgate	(	C &&	code,
		size_t	j )

Definition at line 4642 of file codes.hpp.

expurgate() [2/5]

template<FieldType T>

auto CECCO::expurgate	(	const EmptyCode< T > &	C,
		const std::vector< size_t > &	v )

Definition at line 4621 of file codes.hpp.

expurgate() [3/5]

template<FieldType T>

LinearCode< T > CECCO::expurgate	(	const LinearCode< T > &	C,
		const std::vector< size_t > &	v )

Definition at line 4611 of file codes.hpp.

expurgate() [4/5]

template<FieldType T>

auto CECCO::expurgate	(	const RepetitionCode< T > &	C,
		const std::vector< size_t > &	v )

Definition at line 4634 of file codes.hpp.

expurgate() [5/5]

template<FieldType T>

auto CECCO::expurgate	(	const ZeroCode< T > &	C,
		const std::vector< size_t > &	v )

Definition at line 4627 of file codes.hpp.

extend() [1/2]

template<class B>

auto CECCO::extend

(

B &&

base

)

Definition at line 4522 of file codes.hpp.

extend() [2/2]

template<class B>

auto CECCO::extend	(	B &&	base,
		size_t	i,
		const Vector< field_t< B > > &	v )

Definition at line 4515 of file codes.hpp.

fac()

template<class T>

T CECCO::fac ( T a )

noexcept

Factorial a!

Template Parameters

T	Integer type

Parameters

a	Non-negative integer

Returns

a! = a * (a-1) * ... * 2 * 1

Definition at line 234 of file helpers.hpp.

fill() [1/4]

template<ComponentType T>

Matrix< T > CECCO::fill ( const Matrix< T > & m, const T & value )

constexpr

Definition at line 3266 of file matrices.hpp.

fill() [2/4]

template<ComponentType T>

Vector< T > CECCO::fill ( const Vector< T > & v, const T & value )

constexpr

Definition at line 1492 of file vectors.hpp.

fill() [3/4]

template<ComponentType T>

Matrix< T > CECCO::fill ( Matrix< T > && m, const T & value )

constexpr

Definition at line 3273 of file matrices.hpp.

fill() [4/4]

template<ComponentType T>

Vector< T > CECCO::fill ( Vector< T > && v, const T & value )

constexpr

Definition at line 1499 of file vectors.hpp.

find_irreducible()

template<FieldType T>

Polynomial< T > CECCO::find_irreducible

(

size_t

degree

)

Sample a random monic irreducible polynomial of degree degree over T.

Tries random polynomials until Polynomial::is_irreducible accepts one. Runtime is bounded in expectation by the density of irreducibles, but unbounded in the worst case; suitable as a modulus for CECCO::Ext.

Definition at line 1606 of file polynomials.hpp.

find_maxima()

template<class T>

std::vector< size_t > CECCO::find_maxima

(

const std::vector< T > &

v

)

Indices of all maximum elements.

Template Parameters

T	Element type (must support operator< for comparison)

Parameters

v	Input vector

Returns

Indices i with v[i] == max(v); empty if v is empty

Uses two passes over v.

Definition at line 138 of file helpers.hpp.

GCD() [1/3]

template<ComponentType T>
requires FieldType<T>

Polynomial< T > CECCO::GCD

(

const std::vector< Polynomial< T > > &

polys

)

Greatest common divisor of a list of polynomials, computed iteratively.

Returns

gcd(p₁, p₂, …, pₙ)

Exceptions

std::invalid_argument

if polys is empty

Definition at line 1341 of file polynomials.hpp.

GCD() [2/3]

template<ComponentType T>
requires FieldType<T>

Polynomial< T > CECCO::GCD	(	Polynomial< T >	a,
		Polynomial< T >	b,
		Polynomial< T > *	s = nullptr,
		Polynomial< T > *	t = nullptr )

Greatest common divisor of two polynomials via the (extended) Euclidean algorithm.

Parameters

a	First polynomial
b	Second polynomial
s	Optional out-pointer for the Bézout coefficient of a
t	Optional out-pointer for the Bézout coefficient of b

Returns

gcd(a, b); if both s and t are non-null, additionally gcd(a, b) = s·a + t·b

Operands are reordered internally so that the higher-degree one drives the recursion.

Definition at line 1299 of file polynomials.hpp.

GCD() [3/3]

template<class T>

T CECCO::GCD ( T a, T b, T * s = nullptr, T * t = nullptr )

constexprnoexcept

Greatest common divisor and optional Bézout coefficients.

Template Parameters

T	Signed integral type

Parameters

a	First integer
b	Second integer
s	Pointer to store Bézout coefficient for a (optional)
t	Pointer to store Bézout coefficient for b (optional)

Returns

Greatest common divisor of a and b

If s and t are non-null, stores coefficients satisfying a*s + b*t = gcd(a,b).

Definition at line 178 of file helpers.hpp.

gen()

std::mt19937 & CECCO::gen ( )

inline

Current thread's random number generator.

Returns

Reference to thread-local random number generator

Equivalent to RNG::get.

Definition at line 127 of file helpers.hpp.

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get_submatrix() [1/2]

template<ComponentType T>

Matrix< T > CECCO::get_submatrix	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j,
		size_t	h,
		size_t	w )

Definition at line 2816 of file matrices.hpp.

get_submatrix() [2/2]

template<ComponentType T>

Matrix< T > CECCO::get_submatrix	(	Matrix< T > &&	M,
		size_t	i,
		size_t	j,
		size_t	h,
		size_t	w )

Definition at line 2822 of file matrices.hpp.

get_subvector() [1/2]

template<ComponentType T>

Vector< T > CECCO::get_subvector ( const Vector< T > & v, size_t start, size_t end )

constexpr

Definition at line 1300 of file vectors.hpp.

get_subvector() [2/2]

template<ComponentType T>

Vector< T > CECCO::get_subvector ( Vector< T > && v, size_t start, size_t end )

constexpr

Definition at line 1305 of file vectors.hpp.

GilbertVarshamovLowerBound()

template<FiniteFieldType T>

size_t CECCO::GilbertVarshamovLowerBound	(	size_t	n,
		size_t	dmin )

Definition at line 215 of file code_bounds.hpp.

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GriesmerUpperBound()

template<FiniteFieldType T>

size_t CECCO::GriesmerUpperBound	(	size_t	n,
		size_t	dmin )

Definition at line 166 of file code_bounds.hpp.

HammingUpperBound()

template<FiniteFieldType T>

long double CECCO::HammingUpperBound	(	size_t	n,
		size_t	dmin )

Definition at line 36 of file code_bounds.hpp.

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HankelMatrix()

template<ComponentType T>

Matrix< T > CECCO::HankelMatrix ( const Vector< T > & v, size_t m, size_t n )

constexpr

m × n Hankel matrix from its anti-diagonal entries

Parameters

v	Anti-diagonal values; length m + n − 1
m	Number of rows
n	Number of columns

Returns

Hankel matrix; each ascending anti-diagonal is constant

Constructed as ToeplitzMatrix(reverse(v), m, n) * ExchangeMatrix(n).

Exceptions

std::invalid_argument

if v.length() != m + n - 1

Definition at line 3563 of file matrices.hpp.

Hasse_derivative() [1/2]

template<ComponentType T>
requires FieldType<T>

Polynomial< T > CECCO::Hasse_derivative ( const Polynomial< T > & poly, size_t s )

constexpr

Definition at line 1156 of file polynomials.hpp.

Hasse_derivative() [2/2]

template<ComponentType T>
requires FieldType<T>

Polynomial< T > CECCO::Hasse_derivative ( Polynomial< T > && poly, size_t s )

constexpr

Definition at line 1165 of file polynomials.hpp.

horizontal_join() [1/3]

template<ComponentType T>

Matrix< T > CECCO::horizontal_join	(	const Matrix< T > &	lhs,
		const Matrix< T > &	rhs )

Definition at line 2842 of file matrices.hpp.

horizontal_join() [2/3]

template<ComponentType T>

Matrix< T > CECCO::horizontal_join	(	Matrix< T > &&	lhs,
		const Matrix< T > &	rhs )

Definition at line 2849 of file matrices.hpp.

horizontal_join() [3/3]

template<ComponentType T>

Matrix< T > CECCO::horizontal_join	(	Matrix< T > &&	lhs,
		Matrix< T > &&	rhs )

Definition at line 2856 of file matrices.hpp.

identical()

template<FieldType L, FieldType R>

bool CECCO::identical	(	const LinearCode< L > &	lhs,
		const LinearCode< R > &	rhs )

Definition at line 4662 of file codes.hpp.

IdentityMatrix()

template<ComponentType T>

Matrix< T > CECCO::IdentityMatrix ( size_t m )

constexpr

m × m identity matrix I_m (tag details::Identity)

Parameters

m	Side length

Returns

Newly constructed identity matrix

Definition at line 3455 of file matrices.hpp.

inner_product()

template<ComponentType T>

T CECCO::inner_product	(	const Vector< T > &	lhs,
		const Vector< T > &	rhs )

Inner product ⟨lhs, rhs⟩ = Σᵢ lhs[i] · rhs[i].

For complex inputs this is the standard product (not the conjugate inner product).

Exceptions

std::invalid_argument

if lengths differ

Definition at line 1513 of file vectors.hpp.

inverse() [1/2]

template<ComponentType T>

Matrix< T > CECCO::inverse

(

const Matrix< T > &

M

)

Definition at line 3308 of file matrices.hpp.

inverse() [2/2]

template<ComponentType T>

Matrix< T > CECCO::inverse

(

Matrix< T > &&

M

)

Definition at line 3315 of file matrices.hpp.

is_prime()

template<class T>

bool CECCO::is_prime ( T a )

constexprnoexcept

Primality test by trial division.

Template Parameters

T	Unsigned integer type

Parameters

a	Number to test for primality

Returns

true if a is prime, false otherwise

Tests odd divisors up to √a. Returns false for a ≤ 1 and even a > 2.

Definition at line 157 of file helpers.hpp.

JohnsonUpperBound()

template<FiniteFieldType T>

long double CECCO::JohnsonUpperBound	(	size_t	n,
		size_t	dmin )

Definition at line 73 of file code_bounds.hpp.

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Kronecker_product() [1/3]

template<ComponentType T>

Matrix< T > CECCO::Kronecker_product	(	const Matrix< T > &	lhs,
		const Matrix< T > &	rhs )

Definition at line 2905 of file matrices.hpp.

Kronecker_product() [2/3]

template<ComponentType T>

Matrix< T > CECCO::Kronecker_product	(	Matrix< T > &&	lhs,
		const Matrix< T > &	rhs )

Definition at line 2912 of file matrices.hpp.

Kronecker_product() [3/3]

template<ComponentType T>

Matrix< T > CECCO::Kronecker_product	(	Matrix< T > &&	lhs,
		Matrix< T > &&	rhs )

Definition at line 2919 of file matrices.hpp.

LCM() [1/2]

template<ComponentType T>
requires FieldType<T>

Polynomial< T > CECCO::LCM	(	const Polynomial< T > &	a,
		const Polynomial< T > &	b )

Least common multiple lcm(a, b) = (a · b) / gcd(a, b).

Definition at line 1357 of file polynomials.hpp.

LCM() [2/2]

template<ComponentType T>
requires FieldType<T>

Polynomial< T > CECCO::LCM

(

const std::vector< Polynomial< T > > &

polys

)

Least common multiple of a list of polynomials, computed iteratively.

Returns

lcm(p₁, p₂, …, pₙ)

Exceptions

std::invalid_argument

if polys is empty

Definition at line 1370 of file polynomials.hpp.

lengthen() [1/2]

template<class B>

auto CECCO::lengthen	(	B &&	base,
		size_t	j,
		const Vector< field_t< B > > &	w )

Definition at line 4555 of file codes.hpp.

lengthen() [2/2]

template<class B>

auto CECCO::lengthen	(	B &&	base,
		size_t	j,
		const Vector< field_t< B > > &	w,
		size_t	i,
		const Vector< field_t< B > > &	v )

Definition at line 4548 of file codes.hpp.

LowerShiftMatrix()

template<ComponentType T>

Matrix< T > CECCO::LowerShiftMatrix ( size_t m )

constexpr

m × m lower shift matrix (ones on the subdiagonal); transpose of UpperShiftMatrix

Parameters

m	Side length

Returns

Matrix with L_{i+1, i} = 1, all other entries 0

Definition at line 3626 of file matrices.hpp.

MacWilliamsIdentity()

template<FiniteFieldType T>

Polynomial< InfInt > CECCO::MacWilliamsIdentity	(	const Polynomial< InfInt > &	A,
		size_t	n,
		size_t	k )

Definition at line 62 of file codes.hpp.

modinv()

template<uint16_t p, class T>

T CECCO::modinv ( T a )

constexprnoexcept

Multiplicative inverse modulo a prime.

Template Parameters

p	Prime modulus (must be prime for correct results)
T	Signed integer type

Parameters

a	Element to invert

Returns

Modular inverse a^(-1) mod p

Uses the extended Euclidean algorithm.

Definition at line 219 of file helpers.hpp.

Monomial()

template<ComponentType T>
requires std::convertible_to<std::decay_t<decltype(a)>, T>

Polynomial< T > CECCO::Monomial ( size_t i, auto && a = T(1) )

constexpr

Monomial a · xⁱ

Parameters

i	Power of x
a	Coefficient (defaults to T(1))

Definition at line 1265 of file polynomials.hpp.

normalize() [1/2]

template<ComponentType T>
requires FieldType<T>

Polynomial< T > CECCO::normalize ( const Polynomial< T > & poly )

constexpr

Definition at line 1188 of file polynomials.hpp.

normalize() [2/2]

template<ComponentType T>
requires FieldType<T>

Polynomial< T > CECCO::normalize ( Polynomial< T > && poly )

constexpr

Definition at line 1197 of file polynomials.hpp.

OnePolynomial()

template<ComponentType T>

Polynomial< T > CECCO::OnePolynomial

(

)

Constant polynomial 1 (cached).

Definition at line 1282 of file polynomials.hpp.

operator!=() [1/4]

template<FieldType L, FieldType R>

bool CECCO::operator!=	(	const LinearCode< L > &	lhs,
		const LinearCode< R > &	rhs )

Definition at line 4657 of file codes.hpp.

operator!=() [2/4]

template<ReliablyComparableType T>

bool CECCO::operator!= ( const Matrix< T > & lhs, const Matrix< T > & rhs )

constexpr

Negation of operator==.

Returns

true iff dimensions or any component differ

Definition at line 3376 of file matrices.hpp.

operator!=() [3/4]

template<ComponentType T>

bool CECCO::operator!= ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1211 of file polynomials.hpp.

operator!=() [4/4]

template<ReliablyComparableType T>

bool CECCO::operator!= ( const Vector< T > & lhs, const Vector< T > & rhs )

constexprnoexcept

Definition at line 1543 of file vectors.hpp.

operator%() [1/2]

template<ComponentType T>

Polynomial< T > CECCO::operator% ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1042 of file polynomials.hpp.

operator%() [2/2]

template<ComponentType T>

Polynomial< T > CECCO::operator% ( Polynomial< T > && lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1049 of file polynomials.hpp.

operator*() [1/32]

template<ComponentType T>

Matrix< T > CECCO::operator* ( const Matrix< T > & lhs, const Matrix< T > & rhs )

constexpr

Definition at line 2706 of file matrices.hpp.

operator*() [2/32]

template<ComponentType T>

Matrix< T > CECCO::operator* ( const Matrix< T > & lhs, const T & rhs )

constexpr

Definition at line 2738 of file matrices.hpp.

operator*() [3/32]

template<ComponentType T>

Polynomial< T > CECCO::operator* ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1000 of file polynomials.hpp.

operator*() [4/32]

template<ComponentType T>

Polynomial< T > CECCO::operator* ( const Polynomial< T > & lhs, const T & rhs )

constexpr

Definition at line 1056 of file polynomials.hpp.

operator*() [5/32]

template<ComponentType T>

Polynomial< T > CECCO::operator* ( const Polynomial< T > & lhs, Polynomial< T > && rhs )

constexpr

Definition at line 1014 of file polynomials.hpp.

operator*() [6/32]

template<ComponentType T>

Polynomial< T > CECCO::operator* ( const Polynomial< T > & lhs, size_t n )

constexpr

Definition at line 1099 of file polynomials.hpp.

operator*() [7/32]

template<ComponentType T>

Matrix< T > CECCO::operator* ( const T & lhs, const Matrix< T > & rhs )

constexpr

Definition at line 2756 of file matrices.hpp.

operator*() [8/32]

template<ComponentType T>

Polynomial< T > CECCO::operator* ( const T & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1070 of file polynomials.hpp.

operator*() [9/32]

template<FieldType T>

T CECCO::operator* ( const T & lhs, const T & rhs )

constexpr

Definition at line 363 of file fields.hpp.

operator*() [10/32]

template<ComponentType T>

Vector< T > CECCO::operator* ( const T & lhs, const Vector< T > & rhs )

constexprnoexcept

Definition at line 1234 of file vectors.hpp.

operator*() [11/32]

template<ComponentType T>

Matrix< T > CECCO::operator* ( const T & lhs, Matrix< T > && rhs )

constexpr

Definition at line 2763 of file matrices.hpp.

operator*() [12/32]

template<ComponentType T>

Polynomial< T > CECCO::operator* ( const T & lhs, Polynomial< T > && rhs )

constexpr

Definition at line 1077 of file polynomials.hpp.

operator*() [13/32]

template<FieldType T>

T CECCO::operator* ( const T & lhs, T && rhs )

constexpr

Definition at line 377 of file fields.hpp.

operator*() [14/32]

template<FieldType T>

T CECCO::operator* ( const T & lhs, uint16_t rhs )

constexpr

Definition at line 391 of file fields.hpp.

operator*() [15/32]

template<ComponentType T>

Vector< T > CECCO::operator* ( const T & lhs, Vector< T > && rhs )

constexprnoexcept

Definition at line 1241 of file vectors.hpp.

operator*() [16/32]

template<ComponentType T>

Vector< T > CECCO::operator* ( const Vector< T > & lhs, const Matrix< T > & rhs )

constexpr

Definition at line 2724 of file matrices.hpp.

operator*() [17/32]

template<ComponentType T>

Vector< T > CECCO::operator* ( const Vector< T > & lhs, const T & rhs )

constexprnoexcept

Definition at line 1216 of file vectors.hpp.

operator*() [18/32]

template<FieldType T>

T CECCO::operator* ( int lhs, T && rhs )

constexpr

Definition at line 412 of file fields.hpp.

operator*() [19/32]

template<ComponentType T>

Matrix< T > CECCO::operator* ( Matrix< T > && lhs, const Matrix< T > & rhs )

constexpr

Definition at line 2713 of file matrices.hpp.

operator*() [20/32]

template<ComponentType T>

Matrix< T > CECCO::operator* ( Matrix< T > && lhs, const T & rhs )

constexpr

Definition at line 2745 of file matrices.hpp.

operator*() [21/32]

template<ComponentType T>

Polynomial< T > CECCO::operator* ( Polynomial< T > && lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1007 of file polynomials.hpp.

operator*() [22/32]

template<ComponentType T>

Polynomial< T > CECCO::operator* ( Polynomial< T > && lhs, const T & rhs )

constexpr

Definition at line 1063 of file polynomials.hpp.

operator*() [23/32]

template<ComponentType T>

Polynomial< T > CECCO::operator* ( Polynomial< T > && lhs, Polynomial< T > && rhs )

constexpr

Definition at line 1021 of file polynomials.hpp.

operator*() [24/32]

template<ComponentType T>

Polynomial< T > CECCO::operator* ( Polynomial< T > && lhs, size_t n )

constexpr

Definition at line 1106 of file polynomials.hpp.

operator*() [25/32]

template<ComponentType T>

Polynomial< T > CECCO::operator* ( size_t n, const Polynomial< T > & rhs )

constexpr

Definition at line 1113 of file polynomials.hpp.

operator*() [26/32]

template<ComponentType T>

Polynomial< T > CECCO::operator* ( size_t n, Polynomial< T > && rhs )

constexpr

Definition at line 1120 of file polynomials.hpp.

operator*() [27/32]

template<FieldType T>

T CECCO::operator* ( T && lhs, const T & rhs )

constexpr

Definition at line 370 of file fields.hpp.

operator*() [28/32]

template<FieldType T>

T CECCO::operator* ( T && lhs, int rhs )

constexpr

Definition at line 405 of file fields.hpp.

operator*() [29/32]

template<FieldType T>

T CECCO::operator* ( T && lhs, T && rhs )

constexpr

Definition at line 384 of file fields.hpp.

operator*() [30/32]

template<FieldType T>

T CECCO::operator* ( uint16_t lhs, const T & rhs )

constexpr

Definition at line 398 of file fields.hpp.

operator*() [31/32]

template<ComponentType T>

Vector< T > CECCO::operator* ( Vector< T > && lhs, const Matrix< T > & rhs )

constexpr

Definition at line 2729 of file matrices.hpp.

operator*() [32/32]

template<ComponentType T>

Vector< T > CECCO::operator* ( Vector< T > && lhs, const T & rhs )

constexprnoexcept

Definition at line 1223 of file vectors.hpp.

operator+() [1/16]

template<ComponentType T>

Matrix< T > CECCO::operator+ ( const Matrix< T > & lhs, const Matrix< T > & rhs )

constexpr

Definition at line 2642 of file matrices.hpp.

operator+() [2/16]

template<ComponentType T>

Matrix< T > CECCO::operator+ ( const Matrix< T > & lhs, Matrix< T > && rhs )

constexpr

Definition at line 2656 of file matrices.hpp.

operator+() [3/16]

template<ComponentType T>

Polynomial< T > CECCO::operator+ ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 943 of file polynomials.hpp.

operator+() [4/16]

template<ComponentType T>

Polynomial< T > CECCO::operator+ ( const Polynomial< T > & lhs, Polynomial< T > && rhs )

constexpr

Definition at line 957 of file polynomials.hpp.

operator+() [5/16]

template<FieldType T>

T CECCO::operator+ ( const T & lhs, const T & rhs )

constexpr

Definition at line 307 of file fields.hpp.

operator+() [6/16]

template<FieldType T>

T CECCO::operator+ ( const T & lhs, T && rhs )

constexpr

Definition at line 321 of file fields.hpp.

operator+() [7/16]

template<ComponentType T>

Vector< T > CECCO::operator+ ( const Vector< T > & lhs, const Vector< T > & rhs )

constexpr

Definition at line 1152 of file vectors.hpp.

operator+() [8/16]

template<ComponentType T>

Vector< T > CECCO::operator+ ( const Vector< T > & lhs, Vector< T > && rhs )

constexpr

Definition at line 1166 of file vectors.hpp.

operator+() [9/16]

template<ComponentType T>

Matrix< T > CECCO::operator+ ( Matrix< T > && lhs, const Matrix< T > & rhs )

constexpr

Definition at line 2649 of file matrices.hpp.

operator+() [10/16]

template<ComponentType T>

Matrix< T > CECCO::operator+ ( Matrix< T > && lhs, Matrix< T > && rhs )

constexpr

Definition at line 2663 of file matrices.hpp.

operator+() [11/16]

template<ComponentType T>

Polynomial< T > CECCO::operator+ ( Polynomial< T > && lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 950 of file polynomials.hpp.

operator+() [12/16]

template<ComponentType T>

Polynomial< T > CECCO::operator+ ( Polynomial< T > && lhs, Polynomial< T > && rhs )

constexpr

Definition at line 964 of file polynomials.hpp.

operator+() [13/16]

template<FieldType T>

T CECCO::operator+ ( T && lhs, const T & rhs )

constexpr

Definition at line 314 of file fields.hpp.

operator+() [14/16]

template<FieldType T>

T CECCO::operator+ ( T && lhs, T && rhs )

constexpr

Definition at line 328 of file fields.hpp.

operator+() [15/16]

template<ComponentType T>

Vector< T > CECCO::operator+ ( Vector< T > && lhs, const Vector< T > & rhs )

constexpr

Definition at line 1159 of file vectors.hpp.

operator+() [16/16]

template<ComponentType T>

Vector< T > CECCO::operator+ ( Vector< T > && lhs, Vector< T > && rhs )

constexpr

Definition at line 1173 of file vectors.hpp.

operator-() [1/16]

template<ComponentType T>

Matrix< T > CECCO::operator- ( const Matrix< T > & lhs, const Matrix< T > & rhs )

constexpr

Definition at line 2674 of file matrices.hpp.

operator-() [2/16]

template<ComponentType T>

Matrix< T > CECCO::operator- ( const Matrix< T > & lhs, Matrix< T > && rhs )

constexpr

Definition at line 2688 of file matrices.hpp.

operator-() [3/16]

template<ComponentType T>

Polynomial< T > CECCO::operator- ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 971 of file polynomials.hpp.

operator-() [4/16]

template<ComponentType T>

Polynomial< T > CECCO::operator- ( const Polynomial< T > & lhs, Polynomial< T > && rhs )

constexpr

Definition at line 985 of file polynomials.hpp.

operator-() [5/16]

template<FieldType T>

T CECCO::operator- ( const T & lhs, const T & rhs )

constexpr

Definition at line 335 of file fields.hpp.

operator-() [6/16]

template<FieldType T>

T CECCO::operator- ( const T & lhs, T && rhs )

constexpr

Definition at line 349 of file fields.hpp.

operator-() [7/16]

template<ComponentType T>

Vector< T > CECCO::operator- ( const Vector< T > & lhs, const Vector< T > & rhs )

constexpr

Definition at line 1184 of file vectors.hpp.

operator-() [8/16]

template<ComponentType T>

Vector< T > CECCO::operator- ( const Vector< T > & lhs, Vector< T > && rhs )

constexpr

Definition at line 1198 of file vectors.hpp.

operator-() [9/16]

template<ComponentType T>

Matrix< T > CECCO::operator- ( Matrix< T > && lhs, const Matrix< T > & rhs )

constexpr

Definition at line 2681 of file matrices.hpp.

operator-() [10/16]

template<ComponentType T>

Matrix< T > CECCO::operator- ( Matrix< T > && lhs, Matrix< T > && rhs )

constexpr

Definition at line 2695 of file matrices.hpp.

operator-() [11/16]

template<ComponentType T>

Polynomial< T > CECCO::operator- ( Polynomial< T > && lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 978 of file polynomials.hpp.

operator-() [12/16]

template<ComponentType T>

Polynomial< T > CECCO::operator- ( Polynomial< T > && lhs, Polynomial< T > && rhs )

constexpr

Definition at line 993 of file polynomials.hpp.

operator-() [13/16]

template<FieldType T>

T CECCO::operator- ( T && lhs, const T & rhs )

constexpr

Definition at line 342 of file fields.hpp.

operator-() [14/16]

template<FieldType T>

T CECCO::operator- ( T && lhs, T && rhs )

constexpr

Definition at line 356 of file fields.hpp.

operator-() [15/16]

template<ComponentType T>

Vector< T > CECCO::operator- ( Vector< T > && lhs, const Vector< T > & rhs )

constexpr

Definition at line 1191 of file vectors.hpp.

operator-() [16/16]

template<ComponentType T>

Vector< T > CECCO::operator- ( Vector< T > && lhs, Vector< T > && rhs )

constexpr

Definition at line 1205 of file vectors.hpp.

operator/() [1/10]

template<ComponentType T>

Matrix< T > CECCO::operator/ ( const Matrix< T > & lhs, const T & rhs )

constexpr

Definition at line 2774 of file matrices.hpp.

operator/() [2/10]

template<ComponentType T>

Polynomial< T > CECCO::operator/ ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1028 of file polynomials.hpp.

operator/() [3/10]

template<ComponentType T>

Polynomial< T > CECCO::operator/ ( const Polynomial< T > & lhs, const T & rhs )

constexpr

Definition at line 1085 of file polynomials.hpp.

operator/() [4/10]

template<FieldType T>

T CECCO::operator/	(	const T &	lhs,
		const T &	rhs )

Definition at line 419 of file fields.hpp.

operator/() [5/10]

template<ComponentType T>

Vector< T > CECCO::operator/ ( const Vector< T > & lhs, const T & rhs )

constexpr

Definition at line 1252 of file vectors.hpp.

operator/() [6/10]

template<ComponentType T>

Matrix< T > CECCO::operator/ ( Matrix< T > && lhs, const T & rhs )

constexpr

Definition at line 2781 of file matrices.hpp.

operator/() [7/10]

template<ComponentType T>

Polynomial< T > CECCO::operator/ ( Polynomial< T > && lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1035 of file polynomials.hpp.

operator/() [8/10]

template<ComponentType T>

Polynomial< T > CECCO::operator/ ( Polynomial< T > && lhs, const T & rhs )

constexpr

Definition at line 1092 of file polynomials.hpp.

operator/() [9/10]

template<FieldType T>

T CECCO::operator/	(	T &&	lhs,
		const T &	rhs )

Definition at line 426 of file fields.hpp.

operator/() [10/10]

template<FieldType T>

Vector< T > CECCO::operator/ ( Vector< T > && lhs, const T & rhs )

constexpr

Definition at line 1259 of file vectors.hpp.

operator<<() [1/8]

template<FieldType T>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Code< T > &	rhs )

Definition at line 4672 of file codes.hpp.

operator<<() [2/8]

template<FiniteFieldType B, MOD modulus, LutMode mode>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Ext< B, modulus, mode > &	e )

Print as the integer label (or ERASURE_MARKER if erased).

Definition at line 3072 of file fields.hpp.

operator<<() [3/8]

template<uint16_t p>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Fp< p > &	e )

Print as the integer label (or ERASURE_MARKER if erased).

Definition at line 2174 of file fields.hpp.

operator<<() [4/8]

template<ComponentType T>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Matrix< T > &	rhs )

Pretty-print the matrix with column alignment and bracket borders.

Returns

Reference to os for chaining

An empty matrix is printed as "(empty matrix)".

Definition at line 3388 of file matrices.hpp.

operator<<() [5/8]

template<ComponentType T>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Polynomial< T > &	rhs )

Definition at line 1216 of file polynomials.hpp.

operator<<() [6/8]

template<SignedIntType T>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Rationals< T > &	e )

Print as "numerator/denominator" (or just "numerator" when denominator is 1).

Single stream insertion for std::setw compatibility.

Definition at line 754 of file fields.hpp.

operator<<() [7/8]

template<FieldType T>

std::ostream & CECCO::operator<<	(	std::ostream &	os,
		const Trellis< T > &	Tr )

Definition at line 538 of file trellises.hpp.

operator<<() [8/8]

template<ComponentType T>

std::ostream & CECCO::operator<< ( std::ostream & os, const Vector< T > & rhs )

noexcept

Stream output as ( c₀, c₁, …, cₙ₋₁ ).

Definition at line 1562 of file vectors.hpp.

operator==() [1/4]

template<FieldType L, FieldType R>

bool CECCO::operator==	(	const LinearCode< L > &	lhs,
		const LinearCode< R > &	rhs )

Definition at line 4652 of file codes.hpp.

operator==() [2/4]

template<ReliablyComparableType T>

bool CECCO::operator== ( const Matrix< T > & lhs, const Matrix< T > & rhs )

constexpr

Equality of two matrices.

Returns

true iff dimensions match and all components are equal

Tag-aware fast paths handle structured operands (e.g. two Toeplitz matrices compare only their first row and column).

Definition at line 3330 of file matrices.hpp.

operator==() [3/4]

template<ComponentType T>

bool CECCO::operator== ( const Polynomial< T > & lhs, const Polynomial< T > & rhs )

constexpr

Definition at line 1206 of file polynomials.hpp.

operator==() [4/4]

template<ReliablyComparableType T>

bool CECCO::operator== ( const Vector< T > & lhs, const Vector< T > & rhs )

constexprnoexcept

Definition at line 1537 of file vectors.hpp.

operator>>() [1/2]

template<class LHS, class RHS>

decltype(auto) CECCO::operator>>	(	LHS &&	lhs,
		RHS &&	rhs )

Function-call chaining: x >> f ≡ f(x).

Template Parameters

LHS	Input type
RHS	Callable on LHS

Parameters

lhs	Input value (perfect-forwarded)
rhs	Callable (perfect-forwarded)

Returns

rhs(lhs)

Selected when RHS is invocable with LHS. Disabled for std::ios_base-derived types to avoid clashing with stream operators. The companion overload below handles the case where the right-hand side is an assignment target.

Definition at line 954 of file blocks.hpp.

operator>>() [2/2]

template<class LHS, class RHS>

RHS & CECCO::operator>>	(	LHS &&	lhs,
		RHS &	dst )

Assignment chaining: x >> dst ≡ dst = x; return dst.

Template Parameters

LHS	Input type
RHS	Assignment target type (assignable from LHS)

Parameters

lhs	Input value
dst	Destination variable

Returns

Reference to dst for continued chaining

Selected only when the callable overload above is not viable, so block calls always win over capture-into-variable when both are possible. Useful for capturing intermediate results in a chain (c >> map >> x >> awgn >> y >> demap >> r;).

Definition at line 974 of file blocks.hpp.

operator^() [1/3]

template<ComponentType T>

Polynomial< T > CECCO::operator^ ( const Polynomial< T > & base, int exponent )

constexpr

Polynomial exponentiation by square-and-multiply.

Returns

base^exponent

Warning

Does not follow C++ precedence for ^: in b * base ^ exponent the parser evaluates (b * base) ^ exponent. Parenthesise as b * (base ^ exponent), or call CECCO::sqm directly.

Definition at line 1394 of file polynomials.hpp.

operator^() [2/3]

template<FieldType T>

T CECCO::operator^ ( const T & base, int exponent )

constexpr

Definition at line 433 of file fields.hpp.

operator^() [3/3]

template<FieldType T>

T CECCO::operator^ ( T && base, int exponent )

constexpr

Definition at line 438 of file fields.hpp.

pad_back() [1/2]

template<ComponentType T>

Vector< T > CECCO::pad_back ( const Vector< T > & v, size_t n )

constexpr

Definition at line 1436 of file vectors.hpp.

pad_back() [2/2]

template<ComponentType T>

Vector< T > CECCO::pad_back ( Vector< T > && v, size_t n )

constexpr

Definition at line 1443 of file vectors.hpp.

pad_front() [1/2]

template<ComponentType T>

Vector< T > CECCO::pad_front ( const Vector< T > & v, size_t n )

constexpr

Definition at line 1422 of file vectors.hpp.

pad_front() [2/2]

template<ComponentType T>

Vector< T > CECCO::pad_front ( Vector< T > && v, size_t n )

constexpr

Definition at line 1429 of file vectors.hpp.

PermutationMatrix()

template<ComponentType T>

Matrix< T > CECCO::PermutationMatrix ( const std::vector< size_t > & perm )

constexpr

Permutation matrix P with P_{i, perm[i]} = 1.

Parameters

perm	Permutation of {0, …, m-1}; m is inferred from perm.size()

Returns

m × m permutation matrix; the identity permutation returns IdentityMatrix

Exceptions

std::invalid_argument

if perm contains out-of-range or duplicate indices

Definition at line 3471 of file matrices.hpp.

PlotkinUpperBound()

template<FiniteFieldType T>

long double CECCO::PlotkinUpperBound	(	size_t	n,
		size_t	dmin )

Definition at line 101 of file code_bounds.hpp.

Here is the call graph for this function:

poly_long_div() [1/2]

template<ComponentType T>

std::pair< Polynomial< T >, Polynomial< T > > CECCO::poly_long_div	(	const Polynomial< T > &	lhs,
		const Polynomial< T > &	rhs )

Definition at line 1127 of file polynomials.hpp.

poly_long_div() [2/2]

template<ComponentType T>

std::pair< Polynomial< T >, Polynomial< T > > CECCO::poly_long_div	(	Polynomial< T > &&	lhs,
		const Polynomial< T > &	rhs )

Definition at line 1133 of file polynomials.hpp.

puncture() [1/6]

template<class C>

auto CECCO::puncture	(	C &&	code,
		size_t	i )

Definition at line 4606 of file codes.hpp.

puncture() [2/6]

template<FieldType T>

auto CECCO::puncture	(	const EmptyCode< T > &	C,
		const std::vector< size_t > &	v )

Definition at line 4580 of file codes.hpp.

puncture() [3/6]

template<FieldType T>

LinearCode< T > CECCO::puncture	(	const LinearCode< T > &	C,
		const std::vector< size_t > &	v )

Definition at line 4568 of file codes.hpp.

puncture() [4/6]

template<FieldType T>

auto CECCO::puncture	(	const RepetitionCode< T > &	C,
		const std::vector< size_t > &	v )

Definition at line 4598 of file codes.hpp.

puncture() [5/6]

template<FieldType T>

auto CECCO::puncture	(	const UniverseCode< T > &	C,
		const std::vector< size_t > &	v )

Definition at line 4592 of file codes.hpp.

puncture() [6/6]

template<FieldType T>

auto CECCO::puncture	(	const ZeroCode< T > &	C,
		const std::vector< size_t > &	v )

Definition at line 4586 of file codes.hpp.

randomize() [1/4]

template<ComponentType T>

Matrix< T > CECCO::randomize

(

const Matrix< T > &

M

)

Definition at line 2788 of file matrices.hpp.

randomize() [2/4]

template<ComponentType T>

Vector< T > CECCO::randomize

(

const Vector< T > &

v

)

Definition at line 1272 of file vectors.hpp.

randomize() [3/4]

template<ComponentType T>

Matrix< T > CECCO::randomize

(

Matrix< T > &&

M

)

Definition at line 2795 of file matrices.hpp.

randomize() [4/4]

template<ComponentType T>

Vector< T > CECCO::randomize

(

Vector< T > &&

v

)

Definition at line 1279 of file vectors.hpp.

reciprocal() [1/2]

template<ComponentType T>

Polynomial< T > CECCO::reciprocal ( const Polynomial< T > & poly )

constexpr

Definition at line 1174 of file polynomials.hpp.

reciprocal() [2/2]

template<ComponentType T>

Polynomial< T > CECCO::reciprocal ( Polynomial< T > && poly )

constexpr

Definition at line 1181 of file polynomials.hpp.

ReigerBurstUpperBound()

size_t CECCO::ReigerBurstUpperBound ( size_t n, size_t ell )

inline

Definition at line 242 of file code_bounds.hpp.

reverse() [1/2]

template<ComponentType T>

Vector< T > CECCO::reverse ( const Vector< T > & v )

constexpr

Definition at line 1478 of file vectors.hpp.

reverse() [2/2]

template<ComponentType T>

Vector< T > CECCO::reverse ( Vector< T > && v )

constexpr

Definition at line 1485 of file vectors.hpp.

reverse_columns() [1/2]

template<ComponentType T>

Matrix< T > CECCO::reverse_columns

(

const Matrix< T > &

M

)

Definition at line 3252 of file matrices.hpp.

reverse_columns() [2/2]

template<ComponentType T>

Matrix< T > CECCO::reverse_columns

(

Matrix< T > &&

M

)

Definition at line 3259 of file matrices.hpp.

reverse_rows() [1/2]

template<ComponentType T>

Matrix< T > CECCO::reverse_rows

(

const Matrix< T > &

M

)

Definition at line 3238 of file matrices.hpp.

reverse_rows() [2/2]

template<ComponentType T>

Matrix< T > CECCO::reverse_rows

(

Matrix< T > &&

M

)

Definition at line 3245 of file matrices.hpp.

rotate_left() [1/2]

template<ComponentType T>

Vector< T > CECCO::rotate_left ( const Vector< T > & v, size_t i )

constexpr

Definition at line 1450 of file vectors.hpp.

rotate_left() [2/2]

template<ComponentType T>

Vector< T > CECCO::rotate_left ( Vector< T > && v, size_t i )

constexpr

Definition at line 1457 of file vectors.hpp.

rotate_right() [1/2]

template<ComponentType T>

Vector< T > CECCO::rotate_right ( const Vector< T > & v, size_t i )

constexpr

Definition at line 1464 of file vectors.hpp.

rotate_right() [2/2]

template<ComponentType T>

Vector< T > CECCO::rotate_right ( Vector< T > && v, size_t i )

constexpr

Definition at line 1471 of file vectors.hpp.

rref() [1/2]

template<FieldType T>

Matrix< T > CECCO::rref

(

const Matrix< T > &

M

)

Definition at line 3294 of file matrices.hpp.

rref() [2/2]

template<FieldType T>

Matrix< T > CECCO::rref

(

Matrix< T > &&

M

)

Definition at line 3301 of file matrices.hpp.

scale_column() [1/2]

template<ComponentType T>

Matrix< T > CECCO::scale_column	(	const Matrix< T > &	M,
		const T &	s,
		size_t	i )

Definition at line 2961 of file matrices.hpp.

scale_column() [2/2]

template<ComponentType T>

Matrix< T > CECCO::scale_column	(	Matrix< T > &&	M,
		const T &	s,
		size_t	i )

Definition at line 2975 of file matrices.hpp.

scale_row() [1/2]

template<ComponentType T>

Matrix< T > CECCO::scale_row	(	const Matrix< T > &	M,
		const T &	s,
		size_t	i )

Definition at line 2954 of file matrices.hpp.

scale_row() [2/2]

template<ComponentType T>

Matrix< T > CECCO::scale_row	(	Matrix< T > &&	M,
		const T &	s,
		size_t	i )

Definition at line 2968 of file matrices.hpp.

Schur_product()

template<ComponentType T>

Vector< T > CECCO::Schur_product	(	const Vector< T > &	lhs,
		const Vector< T > &	rhs )

Schur (component-wise) product.

Exceptions

std::invalid_argument

if lengths differ

Definition at line 1526 of file vectors.hpp.

set_component() [1/3]

template<ComponentType T>
requires std::convertible_to<std::decay_t<decltype(M)>, Matrix<T>>

Matrix< T > CECCO::set_component	(	auto &&	M,
		size_t	i,
		size_t	j,
		const T &	c )

Definition at line 2807 of file matrices.hpp.

set_component() [2/3]

template<ComponentType T>

Vector< T > CECCO::set_component	(	const Vector< T > &	v,
		size_t	i,
		const T &	c )

Definition at line 1286 of file vectors.hpp.

set_component() [3/3]

template<ComponentType T>

Vector< T > CECCO::set_component	(	Vector< T > &&	v,
		size_t	i,
		const T &	c )

Definition at line 1293 of file vectors.hpp.

set_submatrix() [1/2]

template<ComponentType T>

Matrix< T > CECCO::set_submatrix	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j,
		const Matrix< T > &	N )

Definition at line 2828 of file matrices.hpp.

set_submatrix() [2/2]

template<ComponentType T>

Matrix< T > CECCO::set_submatrix	(	Matrix< T > &&	M,
		size_t	i,
		size_t	j,
		const Matrix< T > &	N )

Definition at line 2835 of file matrices.hpp.

set_subvector() [1/2]

template<ComponentType T>

Vector< T > CECCO::set_subvector ( Vector< T > && v, size_t start, const Vector< T > & w )

constexpr

Definition at line 1315 of file vectors.hpp.

set_subvector() [2/2]

template<ComponentType T>

Vector< T > CECCO::set_subvector ( Vector< T > v, size_t start, const Vector< T > & w )

constexpr

Definition at line 1310 of file vectors.hpp.

shorten()

template<class B>

auto CECCO::shorten	(	B &&	base,
		size_t	j,
		size_t	i )

Definition at line 4647 of file codes.hpp.

showall()

std::ostream & CECCO::showall ( std::ostream & os )

inline

Definition at line 115 of file codes.hpp.

showbasic()

std::ostream & CECCO::showbasic ( std::ostream & os )

inline

Definition at line 105 of file codes.hpp.

Here is the caller graph for this function:

showmost()

std::ostream & CECCO::showmost ( std::ostream & os )

inline

Definition at line 110 of file codes.hpp.

showspecial()

std::ostream & CECCO::showspecial ( std::ostream & os )

inline

Definition at line 120 of file codes.hpp.

SingletonUpperBound()

size_t CECCO::SingletonUpperBound ( size_t n, size_t dmin )

inline

Definition at line 158 of file code_bounds.hpp.

sqm()

template<class T>

T CECCO::sqm ( T b, int e )

constexpr

Exponentiation by square-and-multiply.

Template Parameters

T	Type supporting multiplication and, for negative exponents, division

Parameters

b	Base value
e	Exponent

Returns

b^e

For negative exponents, computes (1/b)^|e|.

Note

Returns T(1) for e = 0.

Definition at line 297 of file helpers.hpp.

SubfieldSubcode() [1/2]

template<class B>

CECCO::SubfieldSubcode

(

B &&

)

-> SubfieldSubcode< B >

SubfieldSubcode() [2/2]

template<class B>

CECCO::SubfieldSubcode

(

const B &

)

-> SubfieldSubcode< B >

supp()

template<ReliablyComparableType T>

std::vector< size_t > CECCO::supp

(

const Vector< T > &

v

)

Support; see Vector::supp for semantics.

Definition at line 1586 of file vectors.hpp.

swap_columns() [1/2]

template<ComponentType T>

Matrix< T > CECCO::swap_columns	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j )

Definition at line 2933 of file matrices.hpp.

swap_columns() [2/2]

template<ComponentType T>

Matrix< T > CECCO::swap_columns	(	Matrix< T > &&	M,
		size_t	i,
		size_t	j )

Definition at line 2947 of file matrices.hpp.

swap_rows() [1/2]

template<ComponentType T>

Matrix< T > CECCO::swap_rows	(	const Matrix< T > &	M,
		size_t	i,
		size_t	j )

Definition at line 2926 of file matrices.hpp.

swap_rows() [2/2]

template<ComponentType T>

Matrix< T > CECCO::swap_rows	(	Matrix< T > &&	M,
		size_t	i,
		size_t	j )

Definition at line 2940 of file matrices.hpp.

ToeplitzMatrix()

template<ComponentType T>

Matrix< T > CECCO::ToeplitzMatrix ( const Vector< T > & v, size_t m, size_t n )

constexpr

m × n Toeplitz matrix from its diagonal entries (tag details::Toeplitz)

Parameters

v	Diagonal values, ordered so that v[i − j + n − 1] sits on entry (i, j); length m + n − 1
m	Number of rows
n	Number of columns

Returns

Toeplitz matrix; each descending diagonal is constant

Exceptions

std::invalid_argument

if v.length() != m + n - 1

Definition at line 3530 of file matrices.hpp.

transpose() [1/2]

template<ComponentType T>

Matrix< T > CECCO::transpose ( const Matrix< T > & M )

constexpr

Definition at line 3280 of file matrices.hpp.

transpose() [2/2]

template<ComponentType T>

Matrix< T > CECCO::transpose ( Matrix< T > && M )

constexpr

Definition at line 3287 of file matrices.hpp.

unaugment()

template<FieldType T, class B>

B CECCO::unaugment

(

const AugmentedCode< T, B > &

C

)

Definition at line 4543 of file codes.hpp.

unerase_column() [1/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_column ( const Matrix< T > & lhs, size_t i )

constexpr

Definition at line 3166 of file matrices.hpp.

unerase_column() [2/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_column ( Matrix< T > && lhs, size_t i )

constexpr

Definition at line 3173 of file matrices.hpp.

unerase_columns() [1/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_columns ( const Matrix< T > & lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3152 of file matrices.hpp.

unerase_columns() [2/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_columns ( Matrix< T > && lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3159 of file matrices.hpp.

unerase_component() [1/4]

template<ComponentType T>

Matrix< T > CECCO::unerase_component ( const Matrix< T > & lhs, size_t i, size_t j )

constexpr

Definition at line 3110 of file matrices.hpp.

unerase_component() [2/4]

template<ComponentType T>

Vector< T > CECCO::unerase_component	(	const Vector< T > &	lhs,
		size_t	i )

Definition at line 1406 of file vectors.hpp.

unerase_component() [3/4]

template<ComponentType T>

Matrix< T > CECCO::unerase_component ( Matrix< T > && lhs, size_t i, size_t j )

constexpr

Definition at line 3117 of file matrices.hpp.

unerase_component() [4/4]

template<ComponentType T>

Vector< T > CECCO::unerase_component	(	Vector< T > &&	lhs,
		size_t	i )

Definition at line 1413 of file vectors.hpp.

unerase_components() [1/2]

template<ComponentType T>

Vector< T > CECCO::unerase_components	(	const Vector< T > &	lhs,
		const std::vector< size_t > &	v )

Definition at line 1392 of file vectors.hpp.

unerase_components() [2/2]

template<ComponentType T>

Vector< T > CECCO::unerase_components	(	Vector< T > &&	lhs,
		const std::vector< size_t > &	v )

Definition at line 1399 of file vectors.hpp.

unerase_row() [1/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_row ( const Matrix< T > & lhs, size_t i )

constexpr

Definition at line 3222 of file matrices.hpp.

unerase_row() [2/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_row ( Matrix< T > && lhs, size_t i )

constexpr

Definition at line 3229 of file matrices.hpp.

unerase_rows() [1/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_rows ( const Matrix< T > & lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3208 of file matrices.hpp.

unerase_rows() [2/2]

template<ComponentType T>

Matrix< T > CECCO::unerase_rows ( Matrix< T > && lhs, const std::vector< size_t > & v )

constexpr

Definition at line 3215 of file matrices.hpp.

unextend()

template<FieldType T, class B>

B CECCO::unextend

(

const ExtendedCode< T, B > &

C

)

Definition at line 4530 of file codes.hpp.

unit_vector()

template<ComponentType T>

Vector< T > CECCO::unit_vector	(	size_t	length,
		size_t	i )

Length-length vector with T(1) at index i and zeros elsewhere.

Exceptions

std::invalid_argument

if i >= length

Definition at line 1552 of file vectors.hpp.

unlengthen()

template<FieldType T, class D>

auto CECCO::unlengthen

(

const ExtendedCode< T, AugmentedCode< T, D > > &

C

)

Definition at line 4563 of file codes.hpp.

UpperBound()

template<FiniteFieldType T>

long double CECCO::UpperBound	(	size_t	n,
		size_t	dmin )

Definition at line 196 of file code_bounds.hpp.

UpperShiftMatrix()

template<ComponentType T>

Matrix< T > CECCO::UpperShiftMatrix ( size_t m )

constexpr

m × m upper shift matrix (ones on the superdiagonal)

Parameters

m	Side length

Returns

Matrix with U_{i, i+1} = 1, all other entries 0

Definition at line 3613 of file matrices.hpp.

VandermondeMatrix()

template<ComponentType T>

Matrix< T > CECCO::VandermondeMatrix ( const Vector< T > & v, size_t m )

constexpr

Vandermonde matrix V_{i, j} = v[j]^i (tag details::Vandermonde).

Parameters

v	Evaluation points; must be pairwise distinct
m	Number of rows (i.e. the highest power is m − 1)

Returns

m × v.length() Vandermonde matrix

Exceptions

std::invalid_argument

if v is empty, has duplicates, or m is zero

Definition at line 3577 of file matrices.hpp.

vertical_join() [1/3]

template<ComponentType T>

Matrix< T > CECCO::vertical_join	(	const Matrix< T > &	lhs,
		const Matrix< T > &	rhs )

Definition at line 2863 of file matrices.hpp.

vertical_join() [2/3]

template<ComponentType T>

Matrix< T > CECCO::vertical_join	(	Matrix< T > &&	lhs,
		const Matrix< T > &	rhs )

Definition at line 2870 of file matrices.hpp.

vertical_join() [3/3]

template<ComponentType T>

Matrix< T > CECCO::vertical_join	(	Matrix< T > &&	lhs,
		Matrix< T > &&	rhs )

Definition at line 2877 of file matrices.hpp.

wH() [1/2]

template<ReliablyComparableType T>

size_t CECCO::wH ( const Matrix< T > & M )

constexpr

Definition at line 2802 of file matrices.hpp.

wH() [2/2]

template<ReliablyComparableType T>

size_t CECCO::wH ( const Vector< T > & v )

constexprnoexcept

Hamming weight; see Vector::wH for semantics.

Definition at line 1580 of file vectors.hpp.

ZeroMatrix()

template<ComponentType T>

Matrix< T > CECCO::ZeroMatrix ( size_t m, size_t n )

constexpr

m × n matrix of zeros (tag details::Zero)

Parameters

m	Number of rows
n	Number of columns

Returns

Newly constructed zero matrix

Definition at line 3444 of file matrices.hpp.

ZeroPolynomial()

template<ComponentType T>

Polynomial< T > CECCO::ZeroPolynomial

(

)

Constant polynomial 0 (cached).

Definition at line 1275 of file polynomials.hpp.

Variable Documentation

ERASURE_MARKER

std::string_view CECCO::ERASURE_MARKER = "X"

inlineconstexpr

Definition at line 445 of file fields.hpp.