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

Abstract: Let $R=\mathbb{Z}_q+u\mathbb{Z}_q$, where $q=p<sup>s$ and $u<sup>2=0$. 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.