 Binary Golay code

The length-$23$ binary Golay code is the cyclic code over ${\mathbb{F}}_2$ generated byIt 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

The Binary Golay code refers to a specific error-correcting code known as the Golay code, which is used in digital communications to protect data against errors during transmission or storage. There are two main types of Golay codes: the (23, 12, 7) binary Golay code and the (24, 12, 8) extended binary Golay code.