Classes of constacyclic codes of length $p^s$ over the ring $F_{p^m}+u F_{p^m}+vF_{p^m}+uvF_{p^m}$

Abstract

In this paper, we study $\lambda$-constacyclic codes of length $p^s$ over the ring $R=F_{p^m}[u,v]/\langle u^2, v^2, uv-vu \rangle$, where $\lambda = (\lambda _1+u\lambda _2)$ and $(\lambda _1+v\lambda _3)$ such that $\lambda _i~;~ i=1,2,3$ are non zero elements of $F_{p^m}$ for prime number p. Complete ideal structure of the rings $R[x]/ \langle x^{p^s} - \lambda \rangle$ has been presented. We have also discussed the dual $\lambda$-constacyclic codes over R. At last, we extend our results to $\lambda$-constacyclic codes of length $2p^s$ over R.