[Jump to code hierarchy]

Pseudo Golay code[13]

Description

Any one of 13 quaternary Type II self-dual linear codes over \(\mathbb{Z}_4\) whose mod-two reduction (mapping \(0,1,2,3\) to \(0,1,0,1\)) yields the Golay code [3; Thm. 11]. Each code has Lee distance 12, Hamming distance 8, and Euclidean distance 16 [3; Thm. 9].

Cousins

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

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: pseudo_golay

Cite as:
“Pseudo Golay code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/pseudo_golay
BibTeX:
@incollection{eczoo_pseudo_golay, title={Pseudo Golay code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/pseudo_golay} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/pseudo_golay

Cite as:

“Pseudo Golay code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/pseudo_golay

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/rings/over_zq/over_z4/linear_over_z4/pseudo_golay.yml.