Skew constacyclic codes over a class of finite commutative semisimple rings

TL;DR

This paper investigates skew constacyclic codes over finite commutative semisimple rings, characterizing their structure and linking them to linear codes over finite fields, leading to the construction of some optimal codes.

Contribution

It characterizes skew constacyclic codes over certain rings and introduces homomorphisms to matrix product codes, enabling the construction of optimal linear codes.

Findings

Automorphism group of the ring is determined.

Skew constacyclic codes are characterized via linear codes over finite fields.

Some optimal linear codes over finite fields are constructed.

Abstract

In this article, we study skew constacyclic codes over a class of finite commutative semisimple rings. The automorphism group of $\mathcal{R}=\prod_{i=1}^t F_q$ is determined, and we characterize skew constacyclic codes over ring by linear codes over finite field. We also define homomorphisms which map linear codes over $\mathcal{R}$ to matrix product codes over $F_q,$ some optimal linear codes over finite fields are obtained.