Constacyclic and Skew Constacyclic Codes Over a Finite Commutative Non-chain Ring

For anPrakash, Om Islam, Habibul Verma, Ram Krishna odd prime p, this article studies the $$\lambda $$ -constacyclic and skew $$\lambda $$ -constacyclic codes of arbitrary length over the finite commutative non-chain ring $$R=\mathbb {F}_{p^m}[u,v,w]/\langle u^{2}-1,v^{2}-1,w^{2}-1,uv-vu,vw-wv,wu-uw\rangle $$ , where $$\lambda $$ is a unit in R. By using the decomposition method, we determine the structure of $$\lambda $$ -constacyclic and skew $$\lambda $$ -constacyclic codes. Also, the necessary and sufficient conditions of these codes to be self-dual are obtained. Further, it is shown that the Gray images of $$\lambda $$ -constacyclic and skew $$\lambda $$ -constacyclic codes of length n over R are quasi-twisted and skew quasi-twisted codes, respectively of length 8n and index 8 over $$\mathbb {F}_{p^m}$$ . Finally, two non-trivial examples are given to validate the obtained results.