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.