有限链环上的双λ-常循环码

Double λ-constacyclic codes over finite chain rings

设R是一个指数为2且极大理想为γ()的有限链环.设λ是R的一个单位.R上码长为r(,s)的一个双λ-常循环码是划分为两部分的一个集合,并且对这两部分进行λ-常循环移位保持码不变.这些码可以看作是R[x]/(xr-λ)×R[x]/(xs-λ)的R[x]-子模.本文确定了R[x]/(xr-λ)×R[x]/(xs-λ)的R[x]-子模这类码的生成多项式,给出了R[x]/(xr-λ)×R[x]/(xs-λ)的R[x]-子模这类码的极小生成元集.举例表明了通过这类码可以得到有限域上一些比较好的线性码.

Let Rbe a finite chain ring with index two and maximal ideal γ（）.Letλbe a unit of R.A doubleλ-constacyclic code of length r（,s）over Ris a set that can be partitioned into two parts that anyλ-constacyclic shift of the coordinates of both parts leaves invariant the code.These codes can be viewed as R[x]-submodules of R[x]/（xr-λ）×R[x]/（xs-λ）.Further,the generator polynomials and minimal generating sets of this family of codes as R[x]-submodules of R[x]/（xr-λ）×R[x]/（xs-λ）are presented.Examples show that some good linear codes over finite fields can be obtained from this family of codes.