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Klemm code[1]

Description

A member of a family of self-dual linear \((4m,4^1 2^{4m-2})_{\mathbb{Z}_4}\) codes. Its generator matrix consists of a sum of the generator matrix of the repetition code and twice the generator matrix of the SPC code [2].

A generator matrix for this code is \begin{align} \begin{pmatrix} 1 & 1 & 1 & \cdots & 1 & 1\\ 0 & 2 & 0 & \cdots & 0 & 2\\ 0 & 0 & 2 & \cdots & 0 & 2\\ 0 & 0 & 0 & \ddots & \vdots & \vdots\\ 0 & 0 & 0 & \cdots & 2 & 2 \end{pmatrix}\,. \tag*{(1)}\end{align}

Cousins

References

[1]
M. Klemm, “Selbstduale Codes �ber dem Ring der ganzen Zahlen modulo 4”, Archiv der Mathematik 53, 201 (1989) DOI
[2]
S. T. Dougherty, P. Gaborit, M. Harada, A. Munemasa, and P. Sole, “Type IV self-dual codes over rings”, IEEE Transactions on Information Theory 45, 2345 (1999) DOI
[3]
Z. X. Wan, Quaternary Codes (WORLD SCIENTIFIC, 1997) DOI
[4]
A. Bonnecaze, P. Sole, C. Bachoc, and B. Mourrain, “Type II codes over Z/sub 4/”, IEEE Transactions on Information Theory 43, 969 (1997) DOI
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Zoo Code ID: klemm

Cite as:
“Klemm code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/klemm
BibTeX:
@incollection{eczoo_klemm, title={Klemm code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/klemm} }
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Cite as:

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

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