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New quantum codes from skew constacyclic codes

New quantum codes from skew constacyclic codes

Authors :
Habibul Islam
Om Prakash
Ram Krishna Verma
Ashutosh Singh
Source :
Advances in Mathematics of Communications. 17:900-919
Publication Year :
2023
Publisher :
American Institute of Mathematical Sciences (AIMS), 2023.

Abstract

For an odd prime \begin{document}$ p $\end{document} and positive integers \begin{document}$ m $\end{document} and \begin{document}$ \ell $\end{document} , let \begin{document}$ \mathbb{F}_{p^m} $\end{document} be the finite field with \begin{document}$ p^{m} $\end{document} elements and \begin{document}$ R_{\ell,m} = \mathbb{F}_{p^m}[v_1,v_2,\dots,v_{\ell}]/\langle v^{2}_{i}-1, v_{i}v_{j}-v_{j}v_{i}\rangle_{1\leq i, j\leq \ell} $\end{document} . Thus \begin{document}$ R_{\ell,m} $\end{document} is a finite commutative non-chain ring of order \begin{document}$ p^{2^{\ell} m} $\end{document} with characteristic \begin{document}$ p $\end{document} . In this paper, we aim to construct quantum codes from skew constacyclic codes over \begin{document}$ R_{\ell,m} $\end{document} . First, we discuss the structures of skew constacyclic codes and determine their Euclidean dual codes. Then a relation between these codes and their Euclidean duals has been obtained. Finally, with the help of a duality-preserving Gray map and the CSS construction, many MDS and better non-binary quantum codes are obtained as compared to the best-known quantum codes available in the literature.

Details

ISSN :
19305338 and 19305346
Volume :
17
Database :
OpenAIRE
Journal :
Advances in Mathematics of Communications
Accession number :
edsair.doi...........3cc8f84cd7e4a9274792201cc3ded8f8
Full Text :
https://doi.org/10.3934/amc.2021028