Binary Golay code
= Binary Golay code
{title2=$G_{23}=[23,12,7]$}
{wiki}
The length-$23$ <binary Golay code> is the <cyclic code> over $\mathbb F_2$ generated by
$$
g(X)=1+X+X^5+X^6+X^7+X^9+X^{11}.
$$
It has <dimension> $12$, <minimum Hamming distance> $7$, and its radius-$3$ <Hamming balls> partition $\mathbb F_2^{23}$. Its <parity extension> has length $24$, <dimension> $12$, and <minimum Hamming distance> $8$.
// Target: algebra.bigb