New quantum codes from constacyclic codes over the ring $ R_{k,m} $

Abstract

<p style='text-indent:20px;'>For any odd prime <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>, we study constacyclic codes of length <inline-formula><tex-math id="M3">\begin{document}$ n $\end{document}</tex-math></inline-formula> over the finite commutative non-chain ring <inline-formula><tex-math id="M4">\begin{document}$ R_{k,m} = \mathbb{F}_{p^m}[u_1,u_2,\dots,u_k]/\langle u^2_i-1,u_iu_j-u_ju_i\rangle_{i\neq j = 1,2,\dots,k} $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M5">\begin{document}$ m,k\geq 1 $\end{document}</tex-math></inline-formula> are integers. We determine the necessary and sufficient condition for these codes to contain their Euclidean duals. As an application, from the dual containing constacyclic codes, several MDS, new and better quantum codes compare to the best known codes in the literature are obtained.</p>