The following functions perform operations on Finite fields vectors considered as code words in a linear code.
WeightVecFFE( vec ) O
returns the weight of the finite field vector vec, i.e. the number of nonzero entries.
DistanceVecFFE( vec1, vec2 ) O
returns the distance between the two vectors vec1 and vec2, which must have the same length and whose elements must lie in a common field. The distance is the number of places where vec1 and vec2 differ.
DistancesDistributionVecFFEsVecFFE( vecs, vec ) O
returns the distances distribution of the vector vec to the vectors in
the list vecs. All vectors must have the same length, and all elements
must lie in a common field. The distances distribution is a list d of
length Length(vec)+1, such that the value d[i] is the number
of vectors in vecs that have distance i+1 to vec.
DistancesDistributionMatFFEVecFFE( mat, f, vec ) O
returns the distances distribution of the vector vec to the vectors in
the vector space generated by the rows of the matrix mat over the
finite field f. The length of the rows of mat and the length of
vec must be equal, and all elements must lie in f. The rows of mat
must be linearly independent. The distances distribution is a list d
of length Length(vec)+1, such that the value d[i] is the
number of vectors in the vector space generated by the rows of mat
that have distance i+1 to vec.
AClosestVectorCombinationsMatFFEVecFFE( mat, f, vec, l, stop ) O
runs through the f-linear combinations of the vectors in the rows of the matrix mat that can be written as linear combinations of exactly l rows (that is without using zero as a coefficient) and returns a vector from these that is closest to the vector vec. The length of the rows of mat and the length of vec must be equal, and all elements must lie in f. The rows of mat must be linearly independent. If it finds a vector of distance at most stop, which must be a nonnegative integer, then it stops immediately and returns this vector.
CosetLeadersMatFFE( mat, f ) O
returns a list of representatives of minimal weight for the cosets of a code. mat must be a check matrix for the code, the code is defined over the finite field f. All rows of mat must have the same length, and all elements must lie in f. The rows of mat must be linearly independent.
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GAP 4 manual