LexiCode( n, d, F )
In this format, Lexicode returns a Lexicode with word length n,
design distance d over F. The code is constructed using the Greedy
algorithm on the lexicographically ordered list of all vectors of length
n over F. Every time a vector is found that has a distance to the
current code of at least d, it is added to the code. This results,
obviously, in a code with minimum distance greater than or equal to d.
gap> C := LexiCode( 4, 3, GF(5) );
a (4,17,3..4)2..4 lexicode over GF(5)
LexiCode( B, d, F )
When called in this format, LexiCode uses the basis B instead of the
standard basis. B is a matrix of vectors over F. The code is
constructed using the Greedy algorithm on the list of vectors spanned by
B, ordered lexicographically with respect to B.
gap> B := [ [Z(2)^0, 0*Z(2), 0*Z(2)], [Z(2)^0, Z(2)^0, 0*Z(2)] ];;
gap> C := LexiCode( B, 2, GF(2) );
a linear [3,1,2]1..2 lexicode over GF(2)
Note that binary Lexicodes are always linear.
The function GreedyCode creates a Greedy code that is not restricted to
a lexicographical order (see GreedyCode).
GAP 3.4.4