65.28 RootsOfCode

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 

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GAP 3.4.4
April 1997