On cyclic codes over ${\mathbb{Z}}_q+u{\mathbb{Z}}_q$

Let $R={\mathbb{Z}}_q+u{\mathbb{Z}}_q$, where $q=p^s$ and $u^2=0$. In this paper, some structural properties of cyclic codes over the ring $R$ are considered. A necessary and sufficient condition for cyclic codes over the ring $R$ to be free is obtained and a BCH-type bound on the minimum Hamming distance for them is also given.