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\((5,40,4)_{\mathbb{Z}_4}\) Pentacode[1]

Description

Nonlinear \((5,40,4)_{\mathbb{Z}_4}\) code over \(\mathbb{Z}_4\) whose codewords are all cyclic permutations and negations of the strings \(01112\), \(03110\), \(21310\), and \(21132\).

Cousins

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Primary Hierarchy

Classical Domain
Ring Kingdom
Ring codeECC
\(q\)-ary code over \(\mathbb{Z}_q\)ECC
Parents
\(q\)-ary code over \(\mathbb{Z}_q\)
Small-distance block codeECC
\((5,40,4)_{\mathbb{Z}_4}\) Pentacode

References

[1]
J. H. Conway and N. J. A. Sloane, “Quaternary constructions for the binary single-error-correcting codes of Julin, Best and others”, Designs, Codes and Cryptography 4, 31 (1994) DOI
[2]
M. Ran and J. Snyders, “On cyclic reversible self-dual additive codes with odd length over Z/sub 2//sup 2/”, IEEE Transactions on Information Theory 46, 1056 (2000) DOI
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Zoo Code ID: pentacode

Cite as:
“\((5,40,4)_{\mathbb{Z}_4}\) Pentacode”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/pentacode, arXiv:2606.11484
BibTeX:
@incollection{eczoo_pentacode,
title={\((5,40,4)_{\mathbb{Z}_4}\) Pentacode},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/pentacode}
}
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Permanent link:
https://errorcorrectionzoo.org/c/pentacode

Cite as:

“\((5,40,4)_{\mathbb{Z}_4}\) Pentacode”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/pentacode, arXiv:2606.11484

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