ℤ2ℤ2[u]ℤ2[u]-additive complementary codes

This paper focuses on mixed alphabet codes on three alphabets, namely, [Formula: see text] and its extension [Formula: see text] with [Formula: see text]. Through the introduction of novel Gray maps, we explore the structure of cyclic codes and constacyclic codes, focusing on the properties of their generators. Our study extends to the development of Linear Complementary Pair (LCP) codes over the ring. In addition, we construct binary linear codes and highlight the important characteristics of their generators. We also present examples of cyclic, constacyclic, and binary linear codes, with a view of their relevance in the context of quantum codes.