Some Results on Cyclic Codes Over ${F}_{2}+v{F}_{2}$

In this paper, we investigate the structure and properties of cyclic codes over the ring
F

₂
+
vF

₂
. We first study the relationship between cyclic codes over
F

₂
+
vF

₂
and binary cyclic codes. Then we prove that cyclic codes over the ring are principally generated, and give the generator polynomial of cyclic codes over the ring. Finally, we obtain the unique idempotent generators for cyclic codes of odd length and determine the number of cyclic codes for a given length
n
over
F

₂
+
vF

₂
.