In this article, we study skew cyclic codes over $R=mathbb{F}_{q}+vmathbb{F}_{q}+v^{2}mathbb{F}_{q}$, where $q=p^{m}$, $p$ is an odd prime and v3=v. We describe the generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over R by a decomposition theorem. We also describe the generator polynomial of the dual of a skew cyclic code over R. Moreover, the idempotent generators of skew cyclic codes over $mathbb{F}_{q}$ and R are considered.

In this article, we investigate the depth distribution and the depth spectra of linear codes over the ring R=F2+uF2+u2F2, where u3=1. By using homomorphism of abelian groups from R to F2 and the generator matrices of linear codes over R, the depth spectra of linear codes of type 8k14k22k3 are obtained. We also give the depth distribution of a linear code C over R. Finally, some examples are presented to illustrate our obtained results.