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New quantum codes from skew constacyclic codes
New quantum codes from skew constacyclic codes
- 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.
- Subjects :
- Ring (mathematics)
Algebra and Number Theory
Computer Networks and Communications
Applied Mathematics
Quantum codes
Order (ring theory)
Microbiology
Prime (order theory)
Combinatorics
Finite field
Cyclic code
Discrete Mathematics and Combinatorics
Dual polyhedron
Commutative property
Mathematics
Subjects
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