Z_p^r上的polyadic码

Polyadic Codes over Z_p^r

设G为有限阿贝尔群, 群环Zp[G]中的理想称为Zpr 上的阿贝尔码, 其中Zpr 为模pr 剩余类环. 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(X∞,X0,X1,…,Xm-1,定义4类码. 这些码中的任一个码都称为Zpr [G]中的m-adic码(polyadic码). 从而把polyadic 阿贝尔码从有限域上推广到Zpr 上,然后给出了环Zpr } 上polyadic阿贝尔码的性质及存在的条件.

Let G be a finite Abelian group, an ideal in the groupring Zp^r [G] is called an Abelian code over Zp^r, where Zp^r, is the ring of integers modulo p^r. For any subset X of G , an ideal IX in Zp^r EG-1 is defined by means of discrete Fourier transformant zeros. For an m- splitting of G , 4 classes codes are defined. Any of these codes is called an m -adic codes（polyadic codes）. Thus polyadic Abelian codes over finite fields are generalized to over the ring Zp^r . Properties and existent conditions for polyadic Abelian codes over Zp^r are then presented.