On ℤ2R-additive codes and their Macwilliams identities

In this paper, we study a type of mixed alphabet codes, called [Formula: see text]-linear codes, where [Formula: see text] with [Formula: see text]. First, we define and discuss several weight enumerators of [Formula: see text]-linear codes, including Hamming weight, Lee weight and symmetrized weight enumerators. MacWilliams identity connects the weight enumerator of codes and their dual codes. Further, we present the MacWilliams identities about Lee weight and complete weight over the ring [Formula: see text]. Finally, several examples are presented to illustrate our main results.