65.5 Comparisons of Codewords

c_1 = c_2
c_1 < c_2

The equality operator = evaluates to true if the codewords c_1 and c_2 are equal, and to false otherwise. The inequality operator < evaluates to true if the codewords c_1 and c_2 are not equal, and to false otherwise.

Note that codewords are equal if and only if their base vectors are equal. Whether they are represented as a vector or polynomial has nothing to do with the comparison.

Comparing codewords with objects of other types is not recommended, although it is possible. If c_2 is the codeword, the other object c_1 is first converted to a codeword, after which comparison is possible. This way, a codeword can be compared with a vector, polynomial, or string. If c_1 is the codeword, then problems may arise if c_2 is a polynomial. In that case, the comparison always yields a false, because the polynomial comparison is called (see Comparisons of Polynomials).

    gap> P := Polynomial(GF(2), Z(2)*[1,0,0,1]);
    Z(2)^0*(X(GF(2))^3 + 1)
    gap> c := Codeword(P, GF(2));
    x^3 + 1
    gap> P = c;        # codeword operation
    true
    gap> c = P;        # polynomial operation
    false
    gap> c2 := Codeword("1001", GF(2));
    [ 1 0 0 1 ]
    gap> c = c2;
    true 

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