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\([4,2,2]_{\mathbb{Z}_6}\) senary code[1]

Description

A self-dual code over \(\mathbb{Z}_6\) that is one of two such codes, up to permutations [1].

A generator matrix for the code is \begin{align} \begin{pmatrix} 1 & 0 & 1 & 2 \\ 0 & 1 & 4 & 1 \end{pmatrix}~. \tag*{(1)}\end{align}

Member of code lists

Primary Hierarchy

Classical Domain
Ring Kingdom
Ring codeECC
\(q\)-ary code over \(\mathbb{Z}_q\)ECC
Linear code over \(\mathbb{Z}_q\)ECC
Dual code over \(\mathbb{Z}_q\)ECC
Self-dual code over \(\mathbb{Z}_q\)ECC
Parents
Self-dual code over \(\mathbb{Z}_q\)
Small-distance block codeECC
\([4,2,2]_{\mathbb{Z}_6}\) senary code

References

[1]
S. T. DOUGHERTY, M. HARADA, and P. SOLÉ, “Self-dual codes over rings and the Chinese remainder theorem”, Hokkaido Mathematical Journal 28, (1999) DOI
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Zoo Code ID: self_dual_z6

Cite as:
“\([4,2,2]_{\mathbb{Z}_6}\) senary code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/self_dual_z6
BibTeX:
@incollection{eczoo_self_dual_z6, title={\([4,2,2]_{\mathbb{Z}_6}\) senary code}, booktitle={The Error Correction Zoo}, year={2026}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/self_dual_z6} }
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Permanent link:
https://errorcorrectionzoo.org/c/self_dual_z6

Cite as:

“\([4,2,2]_{\mathbb{Z}_6}\) senary code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/self_dual_z6

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/rings/over_zq/dual/self_dual_z6.yml.