Golay code[1]


A \([23, 12, 7]\) perfect binary linear code with connections to various areas of mathematics, e.g., lattices [2] and sporadic simple groups [3]. Adding a parity bit to the code results in the \([24, 12, 8]\) extended Golay code. Up to equivalence, both codes are unique for their respective parameters.

To construct the Golay code, one can use the great dodecahedron to generate codewords by placing message bits on the faces and calculating the parity bits that live on the 12 vertices of the inner icosahedron.


Majority decoding for the extended Golay code [4].Decoder for the extended Golay code using the hexacode [5].Both Golay codes have a trellis representation and can thus be decoded using trellis decoding [6][7].Bounded-distance decoder requiring at most 121 real operations [8].


Extended Golay code used in the Voyager 1 and 2 spacecraft, transmitting hundreds of color pictures of Jupiter and Saturn in their 1979, 1980, and 1981 fly-bys [9].Extended Golay code used in American military standards for automatic link establishment in high frequency radio systems [10].Proofs of the quantum mechanical Kochen-Specker theorem [11].


The automorphism group of the Golay code is the Mathieu group \(\mathcal{M}_{23}\), and the automorphism group of the extended Golay code is the Mathieu group \(\mathcal{M}_{24}\), two of the sporadic simple groups.




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Zoo Code ID: golay

Cite as:
“Golay code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/golay
@incollection{eczoo_golay, title={Golay code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/golay} }
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“Golay code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/golay

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/bits/cyclic/golay.yml.