Skew Cyclic Codes of Length $\ p^s$ over ${\mathbb {F}}_{p^{m}}+u{\mathbb {F}}_{p^m}$

Abstract

Dinh (J Algebra 324:940–950, 2010) characterized constacyclic codes of length $p^s$ over $R_2= {\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$, where $u^2=0$. This idea has been generalized to skew constacyclic codes by many authors. In this paper, we provide new methods to characterize the structure of skew cyclic codes of length $p^s$ over $R_2= {\mathbb {F}}_{p^m}+u{\mathbb {F}}_{p^m}$. As a special case, if we restrict our attention to the polynomial rings ${\mathbb {F}}_{p^m}[x]$ and $R_2[x]$, we obtain most of results appeared in the above paper for cyclic codes.