65.75 BinaryGolayCode

BinaryGolayCode()

BinaryGolayCode returns a binary Golay code. This is a perfect [23,12,7] code. It is also cyclic, and has generator polynomial g(x)=1+x^2+x^4+x^5+x^6+x^{10}+x^{11}. Extending it results in an extended Golay code (see ExtendedBinaryGolayCode). There's also the ternary Golay code (see TernaryGolayCode).

    gap> BinaryGolayCode();
    a cyclic [23,12,7]3 binary Golay code over GF(2)
    gap> ExtendedBinaryGolayCode() = ExtendedCode(BinaryGolayCode());
    true
    gap> IsPerfectCode(BinaryGolayCode());
    true 

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