(1 + u) constacyclic and cyclic codes over \(F_{2} + uF_{2}\) (Q2371062)

The authors consider cyclic and \((1+u)\)-constacyclic codes over the ring of four elements \(\mathbb{Z}_2+u\mathbb{Z}_2=\{0,1,u,u+1\},\) where \(u^2=0.\) They prove that the Gray image of a linear \((1+u)\)-constacyclic code is a distance invariant binary linear cyclic code. In the case when the block length is odd, any binary code which is an image of a linear cyclic code over \(\mathbb{Z}_2+u\mathbb{Z}_2\) under the Gray mapping is equivalent to a linear cyclic code.