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

For any odd prime \begin{document}$ p $\end{document} , we study constacyclic codes of length \begin{document}$ n $\end{document} over the finite commutative non-chain ring \begin{document}$ 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} $\end{document} , where \begin{document}$ m,k\geq 1 $\end{document} 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.