Skew constacyclic codes over a non-chain ring ${\mathbb{F}}_q[u,v]/⟨f(u),g(v),uv-vu⟩$

Abstract

Let $f(u)$ and $g(v)$ be two polynomials of degree $k$ and $\ell$ respectively, not both linear, which split into distinct linear factors over ${\mathbb{F}}_q$. Let $$\begin{gathered} \mathcal{R}={\mathbb{F}}_q[u,v]/⟨f(u),g(v), \\ uv-vu⟩ \end{gathered}$$ be a finite commutative non-chain ring. In this paper, we study $\psi$-skew cyclic and ${\theta }_t$-skew constacyclic codes over the ring $\mathcal{R}$ where $\psi$ and ${\theta }_t$ are two automorphisms defined on $\mathcal{R}$.

15 pages