(1 − uv)-constacyclic codes over $\mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p $

Abstract

Constacyclic codes are an important class of linear codes in coding theory. Many optimal linear codes are directly derived from constacyclic codes. In this paper, (1 − uv)-constacyclic codes over the local ring \(\mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p \) are studied. It is proved that the image of a (1 − uv)-constacyclic code of length n over \(\mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p \) under a Gray map is a distance invariant quasi-cyclic code of index p2 and length p3n over \(\mathbb{F}_p \). Several examples of optimal linear codes over \(\mathbb{F}_p \) from (1 − uv)-constacyclic codes over \(\mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p \) are given.