Which binary error-correcting code has parameters [24, 12, 8]?

The binary error-correcting code with parameters [24, 12, 8] is the extended binary Golay code.

In coding theory, the three numbers mean that each codeword has length 24, the code carries 12 independent bits of information, and its minimum Hamming distance is 8. That distance lets the code correct up to three bit errors or detect up to seven, provided the usual decoding assumptions apply.

The code is usually written G24 and is closely related to the perfect binary Golay code G23, whose parameters are [23, 12, 7]. G23 can be obtained by deleting one coordinate from G24; adding a parity bit reverses the process. The extended code is especially elegant because every codeword has weight 0, 8, 12, 16, or 24. Weight-8 codewords are called octads.

The Golay code has deep links to the Steiner system S(5,8,24), the Leech lattice, and the sporadic Mathieu group M24, which acts as its automorphism group. It also had practical significance in spacecraft communications, including data transmission associated with NASA’s Voyager missions. BCH, Reed–Solomon, and Hamming codes are different code families, not the [24,12,8] binary Golay code.