GeneralizedSrivastavaCode( a, w, z, F )
GeneralizedSrivastavaCode( a, w, z, t, F )
GeneralizedSrivastavaCode returns a generalized Srivastava code with
parameters a, w, z, t. <a> = a_1, ..., a_n and <w> = w_1, ...,
w_s are lists of n+s distinct elements of <F>=GF(q^m), z is a list
of length n of nonzero elements of GF(q^m). The parameter t
determines the designed distance: d geq st + 1. The parity check
matrix of this code has entries of the form z_i over (a_i - w_l)^k
VerticalConversionFieldMat converts this matrix to a matrix with
entries in GF(q) (see VerticalConversionFieldMat). The default for
t is 1. The original Srivastava codes (see SrivastavaCode) are a
special case t=1, z_i=a_i^mu for some mu.
gap> a := Filtered( Elements( GF(2^6) ), e -> e in GF(2^3) );;
gap> w := [ Z(2^6) ];; z := List( [1..8], e -> 1 );;
gap> C := GeneralizedSrivastavaCode( a, w, z, 1, GF(64) );
a linear [8,2,2..5]3..4 generalized Srivastava code over GF(2)
GAP 3.4.4