Skew Constacyclic and LCD Codes over ${\mathbb{F}}_q+v{\mathbb{F}}_q$

Abstract

The aim of this paper is to give conditions for the equivalency between skew constacyclic codes, skew cyclic codes and skew negacyclic codes defined over semi-local rings. Also, we provide construction and an enumeration of Euclidean and Hermitian skew LCD cyclic codes over ${\mathbb{F}}_{p^t}+v{\mathbb{F}}_{p^t}$. Several optimal LCD codes are obtained from Gray images of LCD skew codes over semi-local rings.