Formula omitted] constacyclic and cyclic codes over [formula omitted

Abstract

We introduce ( 1 + u ) constacyclic and cyclic codes over the ring F 2 + u F 2 = { 0 , 1 , u , u ̄ = u + 1 } , where u 2 = 0 , and study them by analogy with the Z 4 case. We prove that the Gray image of a linear ( 1 + u ) constacyclic code over F 2 + u F 2 of length n is a binary distance invariant linear cyclic code. We also prove that, if n is odd, then every binary code which is the Gray image of a linear cyclic code over F 2 + u F 2 of length n is equivalent to a linear cyclic code.