Constacyclic code 

Also known as Twisted 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 \(\alpha c_n, c_1, \cdots, c_{n-1} \in C\). A \(-1\)-constacyclic code is called negacyclic.

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References

[1]
E. R. Berlekamp, Algebraic Coding Theory (WORLD SCIENTIFIC, 2014) DOI
[2]
M. GRASSL, T. BETH, and M. RÖTTELER, “ON OPTIMAL QUANTUM CODES”, International Journal of Quantum Information 02, 55 (2004) arXiv:quant-ph/0312164 DOI
[3]
R. Li and Z. Xu, “Construction of[[n,n−4,3]]qquantum codes for odd prime powerq”, Physical Review A 82, (2010) arXiv:0906.2509 DOI
[4]
X. He, L. Xu, and H. Chen, “New \(q\)-ary Quantum MDS Codes with Distances Bigger than \(\frac{q}{2}\)”, (2015) arXiv:1507.08355
[5]
L. Lu et al., “New Quantum MDS codes constructed from Constacyclic codes”, (2018) arXiv:1803.07927
[6]
G. G. La Guardia, “New Quantum MDS Codes”, IEEE Transactions on Information Theory 57, 5551 (2011) DOI
[7]
X. Kai, S. Zhu, and P. Li, “Constacyclic Codes and Some New Quantum MDS Codes”, IEEE Transactions on Information Theory 60, 2080 (2014) DOI
[8]
B. Chen, S. Ling, and G. Zhang, “Application of Constacyclic Codes to Quantum MDS Codes”, IEEE Transactions on Information Theory 61, 1474 (2015) DOI
[9]
X. Kai and S. Zhu, “New Quantum MDS Codes From Negacyclic Codes”, IEEE Transactions on Information Theory 59, 1193 (2013) DOI
[10]
R. Dastbasteh et al., “An infinite class of quantum codes derived from duadic constacyclic codes”, (2024) arXiv:2312.06504
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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} }
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“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/symmetry/twisted/constacyclic.yml.