Given a code C, return the number of codewords belonging to C.

Given a code C and a positive integer i, return the i-th generator of C.

Given an [n, k] linear code C, return all the possible information sets of C as a (sorted) sequence of sequences of column indices. Each inner sequence contains a maximal set of indices of linearly independent columns in the generator matrix of C.

Field(C) : Code -> FldFin

The underlying field (or alphabet) K of the code C.

The ambient space of C, i.e. the generic vector space V in which C is contained.

The basis of the linear code C, returned as a sequence of elements of C.

The basis matrix for the linear code C, returned as an element of Hom(U, V) where U is the information space of C and V is the ambient space of C.

Given a cyclic code C, return the check polynomial of C. If g(x) is the generator polynonmial of C and h(x) is the check polynomial of C, then g(x)h(x) = 0 (mod x^n - 1), where n is the length of C.

The dimension k of the [n, k] linear code C.

The generators for the linear code C, returned as a set.

The generator matrix for the linear code C, returned as an element of Hom(U, V) where U is the information space of C and V is the ambient space of C.

Given a cyclic code C, return the generator polynomial of C. The generator polynomial of C is a divisor of x^n - 1, where n is the length of C.

Given an [n, k] code C, return the generic [n, n, 1] code in which C is contained.

Given a cyclic code C, return the (polynomial) idempotent of C. If c(x) is the idempotent of C, then c(x)^(2) = 0 (mod x^n - 1), where n is the length of C.

Given an [n, k] linear code C, return the current information set for C. The information set for C is an ordered set of k linearly independent columns of the generator matrix, such that the generator matrix is the identity matrix when restricted to these columns. The information set is returned as a sequence of k integers, giving the numbers of the columns that correspond to the information set.

Given an [n, k] linear code C, return the k-dimensional vector space U which is the space of information vectors for the code C.

Given an [n, k] code C, return the block length n of C.

Ngens(C) : Code -> RngIntElt

The number of generators (which equals the dimension k) of the [n, k] linear code C.

The parity check matrix for the code C, returned as an element of Hom(V, U).

Given an word v belonging to the code C, return the ambient space V of C.

A random codeword of C.

Given an word w belonging to the [n, k] code C, return its support as a subset of the integer set { 1 .. n }. The support of w consists of the coordinates at which w has non-zero entries.

Given an [n, k] linear code C, return the (n - k)-dimensional vector space W, which is the space of syndrome vectors for the code C.

KSpace(C) : Code -> ModTupFld

Given an [n, k] linear code C, defined as a subspace U of the n-dimensional space V, return U as a subspace of V with basis corresponding to the rows of the generator matrix for C.