RootsOfCode( C )
RootsOfCode returns a list of all zeros of the generator polynomial of
a cyclic code C. These are finite field elements in the splitting field
of the generator polynomial, GF(q^m), m is the multiplicative order
of the size of the base field of the code, modulo the word length.
The reverse proces, constructing a code from a set of roots, can be
carried out by the function RootsCode (see RootsCode).
gap> C1 := ReedSolomonCode( 16, 5 );
a cyclic [16,12,5]3..4 Reed-Solomon code over GF(17)
gap> RootsOfCode( C1 );
[ Z(17), Z(17)^2, Z(17)^3, Z(17)^4 ]
gap> C2 := RootsCode( 16, last );
a cyclic [16,12,5]3..4 code defined by roots over GF(17)
gap> C1 = C2;
true
GAP 3.4.4