Research On The Linear Codes And Their Macwilliams Identity Over Two Classes Of The Finite Rings

In this paper, we mainly study the MacWilliams identities of linear codes and constacyclic codes over two classes of finite rings. The details are given as follows:(1) We study linear codes over the ring Z4+vZ4(v2= v) about MacWilliams identities of t-Lee weight.First of all give the linear codes over the ring R1 and it’s Gray map,get the Lee weight over the ring Rl, next give the definition of t-Lee weight enumerator, and and further determine the ring between linear codes and their dual codes based on t-Lee weight polynomial MacWilliams identities.(2) We study the MacWilliams identities of linear codes over the ring R= R+R(v2=1),where R is finite chain ring with maximal ideal (λ),l be the nilpotency of (λ), p is the characteristic of the residue field R/(λ) and p is an odd.then define Lee weight enumerator、Hamming weight enumerator、generalized symmetrized weight enumerator and full weight enumerator of these codes, then study the MacWilliams identities between linear codes and their dual over the ring R+vR with respect to these weight enumerator.(3) We give a class of constacyclic codes over the ring R= R+vR, R is a finite chain ring with maximal ideal (λ). Define homogeneous weight and Gray weight over this ring, structure and properties of constacyclic over the ring 91 are given,the structure is also given.