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Karlin double circulant code[1]

Description

Member of the family of \([2m+2,m+1]\) double circulant codes such that \(m\) is prime of the form \(8k+3\) for some \(k\), and \(2m+2\) is a multiple of eight. See [2; Ch. 16] for their generator matrix.

Cousins

Primary Hierarchy

Parents
Karlin double circulant codes are self-dual doubly even codes [2; Ch. 16]
Karlin double circulant code
Children
The extended Golay code is equivalent to the Karlin double circulant code for \(m=11\) [2; Ch. 16].
The extended Hamming code is equivalent to the Karlin double circulant code for \(m=3\) [2; Ch. 16].

References

[1]
M. Karlin, “New binary coding results by circulants”, IEEE Transactions on Information Theory 15, 81 (1969) DOI
[2]
F. J. MacWilliams and N. J. A. Sloane. The theory of error correcting codes. Elsevier, 1977.
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Zoo Code ID: karlin

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

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/cyclic/karlin.yml.