Skew Cyclic Codes over the Non-Chain ring $\mathcal{R}_q=\mathbb{F}_q[v]/\langle v^{2}+1\rangle$

Abstract

In this paper, we investigate the algebraic structure of the non-local ring $\mathcal{R}_q = \mathbb{F}_q[v]/\langle v^{2}+1\rangle$ and identify the automorphisms of this ring to study the algebraic structure of the skew cyclic codes and their duals over it.