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

In this article, we investigate properties of cyclic codes over a finite non-chain ring $\mathbb{F}q+v\mathbb{F}q+v^{2\mathbb{F}q+v3\mathbb{F}q+v4\mathbb{F}_q,$} 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 $\mathbb{F}_q.$