Skew-constacyclic codes over $\frac{{\mathbb{F}}_q[v]}{⟨v^q-v⟩}$

Abstract

In this paper, the investigation on the algebraic structure of the ring $\frac{{\mathbb{F}}_q[v]}{⟨v^q-v⟩}$ and the description of its automorphism group, enable to study the algebraic structure of codes and their dual over this ring. We explore the algebraic structure of skew-constacyclic codes, by using a linear Gray map and we determine their generator polynomials. Necessary and sufficient conditions for the existence of self-dual skew cyclic and self-dual skew negacyclic codes over $\frac{{\mathbb{F}}_q[v]}{⟨v^q-v⟩}$ are given.