Reversible cyclic codes over ${\mathbb{F}}_q+u{\mathbb{F}}_q$

Let $q$ be a power of a prime $p$. In this paper, we study reversible cyclic codes of arbitrary length over the ring $R={\mathbb{F}}_q+u{\mathbb{F}}_q$, where $u^2=0modq$. First, we find a unique set of generators for cyclic codes over $R$, followed by a classification of reversible cyclic codes with respect to their generators. Also, under certain conditions, it is shown that dual of reversible cyclic code is reversible over ${\mathbb{Z}}_2+u{\mathbb{Z}}_2$. Further, to show the importance of these results, some examples of reversible cyclic codes are provided.