# Skew constacyclic codes over a non-chain ring $\mathbb{F}_{q}[u,v]/\langle f(u),g(v), uv-vu\rangle$

## TL;DR

This paper investigates skew constacyclic codes over a specific non-chain ring constructed from polynomials over a finite field, focusing on their algebraic structure and properties.

## Contribution

It introduces and analyzes $ heta_t$-skew constacyclic codes over a non-chain ring formed by polynomials, extending the theory of skew codes to new algebraic settings.

## Key findings

- Characterization of $ heta_t$-skew constacyclic codes over the ring
- Conditions for code invariance under automorphisms
- Structural properties of codes over non-chain rings

## 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 $\mathcal{R}=\mathbb{F}_{q}[u,v]/\langle f(u),g(v),\\uv-vu\rangle$ 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 $\mathcal{R}$.