(1+v)-Constacyclic codes over

In this work, (1+v)-constacyclic codes over the ring F 2 + u F 2 + v F 2 + uv F 2 are studied. (1+v)-constacyclic codes over F 2 + u F 2 + v F 2 + uv F 2 of odd lengths are characterized with the help of cyclic codes over F 2 + u F 2 + v F 2 + uv F 2 . A natural Gray map from ( F 2 + u F 2 + v F 2 + uv F 2 ) n to ( F 2 + u F 2 ) 2 n is introduced and it is shown that the image under this map of (1+v)-constacyclic codes over F 2 + u F 2 + v F 2 + uv F 2 are cyclic codes over F 2 + u F 2 . Also a substantial number of optimal binary linear codes are obtained as the images of (1+v)-constacyclic codes over F 2 + u F 2 + v F 2 + uv F 2 .