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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. Anecessary and sufficient condition for cyclic codes over the ring $R$ to befree is obtained and a BCH-type bound on the minimum Hamming distance for themis also given.

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