$\left(1+\lambda uvw \right) $-constacyclic codes over the ring $\F_q[u,v,w]/ \langle u^2, v^2, w^2, uv-vu, vw-wv, uw-wu \rangle$

Abstract

In this paper, we  find  constacyclic codes over the ring  $R_{u^2, v^2, w^2, q}= \F_q[u,v,w]/\langle u^2,$ $v^2, w^2$, $uv-vu, vw-wv, uw-wu \rangle$ of length $q-1$ where $q$ is a power of prime number. We find minimal spanning set and a unique set of generators for these codes. We also shows that Gray image of $\left(1+\lambda uvw \right) $-constacyclic codes of length $N$ over $R_{u^2, v^2, w^2, q} $ are 8-quasicyclic binary linear code of length $8N$ over $\F_q$.