Quasi-cyclic code[1]
Description
A code \(C\) of length \(n\) over an alphabet is quasi-cyclic if, for each codeword \(c_1 \cdots c_{\ell} c_{\ell+1} \cdots c_n\), the string \(c_{n-\ell+1} \cdots c_n c_1 \cdots c_{n-\ell}\) where each entry is cyclically shifted by \(\ell\) increments is also a codeword.
The generator of an \([mn_0,mk_0]\) quasi-cyclic linear code is representable as a block matrix of \(m \times m\) circulant matrices [2].
Notes
A database of quasi-cyclic codes with searchable parameters such as block length and dimension is constructed and displayed here.
Parent
Children
- Cyclic code — Quasi-cyclic codes with \(\ell=1\) are cyclic.
- Skew-cyclic code — Under certain conditions, there is an equivalent quasi-cyclic code for every skew-cyclic code [3].
References
- [1]
- R. Townsend and E. Weldon, “Self-orthogonal quasi-cyclic codes”, IEEE Transactions on Information Theory 13, 183 (1967). DOI
- [2]
- Thomas A. Gulliver, Construction of quasi-cyclic codes, Thesis, University of New Brunswick, 1989.
- [3]
- I. Siap et al., “Skew cyclic codes of arbitrary length”, International Journal of Information and Coding Theory 2, 10 (2011). DOI
Page edit log
- Victor V. Albert (2022-06-14) — most recent
- Micah Shaw (2022-06-13)
- Nolan Coble (2021-11-27)
Zoo code information
Cite as:
“Quasi-cyclic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quasi_cyclic