Z2[u]Z2[u]-Additive codes

Abstract

In this paper, we study mixed alphabet codes over two alphabets [Formula: see text], and its extension [Formula: see text], [Formula: see text]. We define new Gray maps, using which we study cyclic codes and obtain the properties of their generators. Further, we construct constacyclic codes, and linear codes, and observe the useful properties of their generators. Finally, we present some examples of cyclic codes and binary linear codes.