Constacyclic codes over F_q + u F_q + v F_q + u v F_q

TL;DR

This paper investigates constacyclic codes over a specific finite ring, characterizing their generator polynomials, duals, and Gray images, contributing to coding theory over complex algebraic structures.

Contribution

It provides a complete characterization of constacyclic codes, their duals, and Gray images over the ring F_q+ u F_q + v F_q + u v F_q, including self-dual cyclic codes.

Findings

Generator polynomials characterized for these codes.

Dual codes and Gray images explicitly described.

Conditions for self-duality in Gray images established.

Abstract

Let q be a prime power and F_q be a finite field. In this paper, we study constacyclic codes over the ring F_q+ u F_q +v F_q+ u v F_q, where u^2=u, v^2=v and uv=vu. We characterized the generator polynomials of constacyclic codes and their duals using some decomposition of this ring. We also define a gray map and characterize the Gray images of self-dual cyclic codes over F_q+uF_q+vF_q+uvF_q.