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valbert4 committed Oct 24, 2024
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logical: q-ary_digits

name: 'Ternary Golay code'
introduced: '\cite{manual:{M. J. E. Golay, \emph{Notes on digital coding}, Proc. IEEE, 37 (1949) 657.}}'
introduced: '\cite{manual:{Veikkaus-Lotto (Veikkaaja) magazine, issues 27, 28, and 33, August-September 1947.},manual:{M. J. E. Golay, \emph{Notes on digital coding}, Proc. IEEE, 37 (1949) 657.}}'

description: |
A \([11,6,5]_3\) perfect ternary linear code with connections to various areas of mathematics, e.g., lattices \cite{doi:10.1007/978-1-4757-6568-7} and sporadic simple groups \cite{preset:MacSlo}.
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- 'Decoder for the extended ternary Golay code using the tetracode \cite{doi:10.1109/TIT.1986.1057197}.'

realizations:
- 'Code used in football pools with at least one good bet \cite{doi:10.1016/0097-3165(91)90024-B,doi:10.1007/BF03025254}. In fact, the code was originally constructed by Juhani Virtakallio and published in the Finnish football pool magazine Veikkaaja \cite{doi:10.1007/BF03025254,doi:10.5948/UPO9781614440215}.'
- 'Code used in football pools with at least one good bet \cite{doi:10.1016/0097-3165(91)90024-B,doi:10.1007/BF03025254}. In fact, the code was originally constructed by Juhani Virtakallio and published in the Finnish football pool magazine Veikkaaja \cite{manual:{Veikkaus-Lotto (Veikkaaja) magazine, issues 27, 28, and 33, August-September 1947.},doi:10.1007/BF03025254,doi:10.5948/UPO9781614440215}.'
- 'Proofs of the quantum mechanical Kochen-Specker theorem \cite{arxiv:2206.04209}.'

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