Cyclic codes over F2 + uF2 + vF2 + uvF2

In this work, we focus on cyclic codes over the ring , 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 and cyclic codes of odd length. Some good binary codes are obtained as the images of cyclic codes over under two Gray maps that are defined. We also characterize the binary images of cyclic codes over in general.