Cyclic and some constacyclic codes over the ring Z4[u]〈u2−1〉

In this paper, we study cyclic codes and constacyclic codes with shift constant (2+u)(2+u) over R=Z4+uZ4R=Z4+uZ4, where u2=1u2=1. We determine the form of the generators of the cyclic codes over this ring and their spanning sets. Considering their Z4Z4 images, we prove that the Z4Z4-image of a (2+u)(2+u)-constacyclic code of odd length is a cyclic code over Z4Z4. We also present many examples of cyclic codes over R   whose Z4Z4-images have better parameters than previously best-known Z4Z4-linear codes.