MacWilliams identities for linear codes over the ring Z4+uZ4 on the Hermitian inner product

Coding theory has so many important applications in cryptogram, communication technology and network security, etc. The MacWilliams type of identities for linear codes over rings are very important research object, becauce they are related to the computation of decoding error probability and error probability of undetectable codes. In this paper, we study linear codes over the ring Z₄ + uZ₄ with u² = 0 . The Hermitian inner product over such ring is defined. New definitions for the complete weight enumerator, the symmetrical weight enumerator, the Lee weight enumerator and the Hamming weight enumerator of linear codes over the ring Z⁴ + uZ₄ for the Hermitian inner product are given. The MacWilliams identities for these weight enumerators are studied.