Invariants

# C : Code -> RngIntElt
Given a code C, return the number of codewords belonging to C.
C . i : Code, RngIntElt -> ModTupRngElt
Name(C, i) : Code, RngIntElt -> ModTupRngElt
Given a code C and a positive integer i, return the i-th generator of C.
Alphabet(C) : Code -> Rng
The underlying ring (or alphabet) R of the code C.
AmbientSpace(C) : Code -> ModTupRng
The ambient space of the code C, i.e., the generic R-space V in which C is contained.
Basis(C) : Code -> [ ModTupRngElt ]
The basis of the linear code C, returned as a sequence of elements of C.
Generators(C) : Code -> { ModTupRngElt }
The generators for the linear code C, returned as a set.
GeneratorMatrix(C) : Code -> ModMatRngElt
The generator matrix for the linear code C. This gives a unique canonical generating set for the code.
Generic(C) : Code -> Code
Given a length n code C over a ring R, return the generic (n, #Rn, 1) code in which C is contained.
Length(C) : Code -> RngIntElt
Given a code C, return the block length n of C.
PseudoDimension(C) : Code -> RngIntElt
NumberOfGenerators(C) : Code -> RngIntElt
Ngens(C) : Code -> RngIntElt
The number of generators (which equals the pseudo-dimension k) of the linear code C.
ParityCheckMatrix(C) : Code -> ModMatRngElt
The parity check matrix for the code C, which can be defined as the canonical generator matrix of the dual of C.
Random(C): Code -> ModTupRngElt
A random codeword of the code C.
RSpace(C) : Code -> ModTupRng
Given a length n 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.
InformationRate(C) : Code -> RngPrElt
Given a code C over a ring with cardinality q, return the information rate of C, that is, the ratio Logq(#C)/n.
V2.28, 13 July 2023