(1+u)(1+u) constacyclic and cyclic codes over F2+uF2F2+uF2

We introduce (1+u)(1+u) constacyclic and cyclic codes over the ring F2+uF2={0,1,u,ū=u+1}, where u2=0u2=0, and study them by analogy with the Z4Z4 case. We prove that the Gray image of a linear (1+u)(1+u) constacyclic code over F2+uF2F2+uF2 of length nn is a binary distance invariant linear cyclic code. We also prove that, if nn is odd, then every binary code which is the Gray image of a linear cyclic code over F2+uF2F2+uF2 of length nn is equivalent to a linear cyclic code.