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 $$\mathbb{F}_q+v\mathbb{F}_q+v<sup>2\mathbb{F}_q+v<sup>3\mathbb{F}_q+v<sup>4\mathbb{F}_q,$$ where $q=p<sup>r,$ $r$ is a positive integer, $p$ is an odd prime, $4 \mid (p-1),$ and $v<sup>5=v.$ As an application, we construct several quantum error correcting codes over the finite field $\mathbb{F}_q.$