120 Cyclic Codes over $Fq+uFq+vFq+uvFq$

In this paper, by studying the polynomial ring $Rn=(Fq+uFq+vFq+uvFq)[x]/(xn−1)$, cyclic codes over the ring $R=Fq+uFq+vFq+uvFq$ are discussed, where the ring R is not a finite chain ring. Finally, when $q=2$, let $S=F2+uF2+vF2+uvF2$, by studying the polynomial ring $Sn=(F2+uF2+vF2+uvF2)[x[/(xn−(1+u))$ and using the corresponding relationship between the (1+u)-consta-cyclic codes over the ring S and the ideals in the ring $Sn$, (1+u)-constacyclic codes over the ring S are characterized.