Z2^r上的Duadic码

Duadic Codes over Z_2~r

设G为有限阿贝尔群,群环Zpr[G]中的理想称为Zpr上的阿贝尔码。对G的任意子集X,由离散Fourier变换和根定义Zpr[G]中的一个理想IX。对于G的m-劈分定义四类码,这些码中的任一个码都称为Zpr[G]中的m-adic码,在此定义的基础上,给出Z2r上Duadic码存在的充分必要条件。

Let G be a finite Abelian group,and an ideal in the grouping Zpr[G] is called an Abelian code over Zpr.For any subset X of G,an ideal X in Zpr[G] is defined by means of discrete Fourier transform and zeros.For an m-splitting of G,4 classes codes are defined.Any of these codes is called an m-adic codes.Thus necessary and sufficient existent conditions for duadic codes over Zr2 are presented.