$\mathbb {Z}_{2}\mathbb {Z}_{2}[u]$ –Cyclic and Constacyclic Codes
İsmail Aydoğdu, Taher Abualrub, İrfan Şiap · IEEE Transactions on Information Theory · 2016
Following the very recent studies on ℤ2ℤ4-additive codes, ℤ2ℤ2[u]-linear codes have been introduced by Aydogdu et al. In this paper, we introduce and study the algebraic structure of cyclic, constacyclic codes and their duals over the R-module Z2αRβwhere R = ℤ2+uℤ2= {0, 1, u, u + 1} is the ring with four elements and u2= 0. We determine the generating independent sets and the types and sizes of both such codes and their duals. Finally, we present a bound and an optimal family of codes attaining this bound and also give some illustrative examples of binary codes that have good parameters which are obtained from the cyclic codes in Z2αRβ.