Cyclic codes over F2+uF2+vF2+uvF2

In this work, we focus on cyclic codes over the ring F2+uF2+vF2+uvF2, which is not a finite chain ring. We use ideas from group rings and works of AbuAlrub et al. in (Des Codes Crypt 42:273–287, 2007) to characterize the ring (F2 + uF2 + vF2 + uvF2)/(x − 1) and cyclic codes of odd length. Some good binary codes are obtained as the images of cyclic codes over F2+uF2+vF2+uvF2 under two Gray maps that are defined. We also characterize the binary images of cyclic codes over F2 + uF2 + vF2 + uvF2 in general.