Let G be a finite Abelian group,an ideal in the groupring Z_(p~r)[G] is called an Abelian code over Z_(p~r), where Z_(p~r) is the ring of integers modulo 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.