Constacyclic code 

Description

A classical code \(C\) of length \(n\) over an alphabet \(R\) is \(\alpha\)-constacyclic (or \(\alpha\)-twisted) if, for each string \(c_1 c_2 \cdots c_n\in C\), the string \(\alpha c_n c_1 \cdots c_{n-1} \in C\).

Parent

Child

  • Cyclic code — Constacyclic codes with \(\alpha=1\) are cyclic.

Cousins

References

[1]
X. Kai, S. Zhu, and P. Li, “Constacyclic Codes and Some New Quantum MDS Codes”, IEEE Transactions on Information Theory 60, 2080 (2014) DOI
[2]
B. Chen, S. Ling, and G. Zhang, “Application of Constacyclic Codes to Quantum MDS Codes”, IEEE Transactions on Information Theory 61, 1474 (2015) DOI
[3]
L. Lu et al., “New Quantum MDS codes constructed from Constacyclic codes”, (2018) arXiv:1803.07927
[4]
R. Dastbasteh et al., “Infinite class of quantum codes derived from duadic constacyclic codes”, (2023) arXiv:2312.06504
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: constacyclic

Cite as:
“Constacyclic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/constacyclic
BibTeX:
@incollection{eczoo_constacyclic, title={Constacyclic code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/constacyclic} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/constacyclic

Cite as:

“Constacyclic code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/constacyclic

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/properties/block/cyclic/constacyclic.yml.