= BCH and parity-extension proof of the binary Golay distance
{c}
A root $\beta$ of the binary <Golay generator polynomial> has order $23$, and the <Frobenius endomorphism> shows that $\beta,\beta^2,\beta^3,\beta^4$ are roots: $2^8\equiv3\pmod{23}$. The <BCH bound> gives <minimum Hamming distance> at least five. The <circular autocorrelation of the binary Golay generator> makes its <parity extension> <doubly even>, excluding original weights five and six. The generator itself has <Hamming weight> seven, proving that the distance is exactly seven.
// Target: algebra.bigb
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