Quantum codes constructed from cyclic codes over the ring ${\mathbb{F}}_q+v{\mathbb{F}}_q+v^2{\mathbb{F}}_q+v^3{\mathbb{F}}_q+v^4{\mathbb{F}}_q$

Abstract

In this article, we investigate properties of cyclic codes over a finite non-chain ring ${\mathbb{F}}_q+v{\mathbb{F}}_q+v^2{\mathbb{F}}_q+v^3{\mathbb{F}}_q+v^4{\mathbb{F}}_q,$ where $q=p^r,$ $r$ is a positive integer, $p$ is an odd prime, $4\mid (p-1),$ and $v^5=v.$ As an application, we construct several quantum error correcting codes over the finite field ${\mathbb{F}}_q.$

14 pages, submitted to the journal at November 28, 2021