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
- Cyclic linear \(q\)-ary code— Karlin double circulant codes can be mapped to extended cyclic and extended quadratic-residue codes over \(GF(4)\) [2; Ch. 16].
- Quadratic-residue (QR) code— Karlin double circulant codes can be mapped to extended cyclic and extended quadratic-residue codes over \(GF(4)\) [2; Ch. 16].
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.
Page edit log
- Victor V. Albert (2025-01-08) — most recent
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.