CAJ | 학술논문

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.
설G위유한아패이군,군배Zp[G]중적이상칭위Zpr상적아패이마,기중Zpr위모pr잉여류배.대G적임의자집X,유리산Fourier변환화근정의Zpr[G]중적일개이상Ix.대우G적m-벽분(X∞,X0,X1,…,Xm-1,정의4류마.저사마중적임일개마도칭위Zpr[G]중적m-adic마(polyadic마).종이파polyadic아패이마종유한역상추엄도Zpr상,연후급출료배Zpr}상polyadic아패이마적성질급존재적조건.
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.