Construction of skew cyclic codes over 픽q+v픽q

In this paper skew cyclic codes over the the family of rings $\mathbb{F}_q+v\mathbb{F}_q$ with $v^2=v$ are studied for the first time in its generality. Structural properties of skew cyclic codes over $\mathbb{F}_q+v\mathbb{F}_q$ are investigated through a decomposition theorem. It is shown that skew cyclic codes over this ring are principally generated. The idempotent generators of skew-cyclic codes over $\mathbb{F}_q$ and $\mathbb{F}_q+v\mathbb{F}_q$ have been considered for the first time in literature. Moreover, a BCH type bound is presented for the parameters of these codes.