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

TL;DR

This paper explores cyclic codes over a specific finite ring and uses their properties to construct quantum error-correcting codes over finite fields, advancing quantum coding theory.

Contribution

It introduces new methods for constructing quantum codes from cyclic codes over a non-chain ring, expanding the toolkit for quantum error correction.

Findings

Properties of cyclic codes over the ring are characterized.

New quantum error-correcting codes are constructed.

Applications demonstrate improved code parameters.

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 $\mathbb{F}_q.$