65.66 GoppaCode

GoppaCode( G, L )

GoppaCode returns a Goppa code from Goppa polynomial G, having coefficients in a Galois Field GF(q^m). L must be a list of elements in GF(q^m), that are not roots of G. The word length of the code is equal to the length of L. The parity check matrix contains entries of the form a_i^j G(a_i), a_i in L. The function VerticalConversionFieldMat converts this matrix to a matrix with entries in GF(q) (see VerticalConversionFieldMat).

    gap> x := Indeterminate( GF(2) );; x.name := "x";;
    gap> G := x^2 + x + 1;; L := Elements( GF(8) );;
    gap> C := GoppaCode( G, L );
    a linear [8,2,5]3 Goppa code over GF(2) 

GoppaCode( G, n )

When called with parameter n, GUAVA constructs a list L of length n, such that no element of L is a root of G.

    gap> x := Indeterminate( GF(2) );; x.name := "x";;
    gap> G := x^2 + x + 1;;
    gap> C := GoppaCode( G, 8 );
    a linear [8,2,5]3 Goppa code over GF(2) 

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