Description
Any one of 13 quaternary extremal Type II self-dual linear codes over \(\mathbb{Z}_4\) of length 24 whose mod-two reduction (mapping \(0,1,2,3\) to \(0,1,0,1\)) is the Golay code [3; Thm. 11]. Each code has Lee distance 12, Hamming distance 8, and Euclidean distance 16 [3; Thm. 9].Cousins
- \([24, 12, 8]\) Extended Golay code— The mod-two reduction (mapping \(0,1,2,3\) to \(0,1,0,1\)) of all pseudo Golay codes yields the extended Golay code; see Ref. [4].
- Combinatorial design— Supports of codewords of any fixed symmetrized type of pseudo Golay codes form a 5-design [5–7].
- \(\Lambda_{24}\) Leech lattice— The Leech lattice can be constructed from pseudo Golay codes via Construction \(A_4\) [3,4].
Member of code lists
Primary Hierarchy
Parents
Pseudo Golay codes are extremal Type II self-dual codes over \(\mathbb{Z}_4\) [3; Thm. 9].
Pseudo Golay code
References
- [1]
- W. C. Huffman, “Decompositions and extremal type II codes over Z/sub 4/”, IEEE Transactions on Information Theory 44, 800 (1998) DOI
- [2]
- P. Gaborit and M. Harada, Designs, Codes and Cryptography 16, 257 (1999) DOI
- [3]
- E. Rains, “Optimal self-dual codes over Z4”, Discrete Mathematics 203, 215 (1999) DOI
- [4]
- G. W. Moore and R. K. Singh, “Beauty And The Beast Part 2: Apprehending The Missing Supercurrent”, (2023) arXiv:2309.02382
- [5]
- T. A. Gulliver and M. Harada, “Extremal double circulant Type II codes over Z4 and construction of 5-(24, 10, 36) designs”, Discrete Mathematics 194, 129 (1999) DOI
- [6]
- M. Harada, “New 5-designs constructed from the lifted Golay code over ?4”, Journal of Combinatorial Designs 6, 225 (1998) DOI
- [7]
- A. Bonnecaze, E. Rains, and P. Solé, “3-Colored 5-Designs and Z4-Codes”, Journal of Statistical Planning and Inference 86, 349 (2000) DOI
Page edit log
- Victor V. Albert (2025-03-26) — most recent
Cite as:
“Pseudo Golay code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/pseudo_golay