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 errorecting codes over the finite field $\mathbb{F}_q.$

翻译：在本篇文章中,我们调查一个有限的非链环的周期代码属性 $\mathbb{Fq+v\mathb{Fq+v2\mathb{Fq+v}3\mathbb{Fq+q+v}4\mathbb{F*q,美元=p ⁇ r,美元是正整数, 美元是奇数, 4\mid(p-1), 美元和 $v ⁇ 5=v.$。 作为一种应用,我们为限定字段构建了若干量子误判代码 $\mathb{F}q。