Module codes in group rings

被引：4

作者：

Hurley, Paul ^{[1
]}

Hurley, Ted ^{[2
]}

机构：

[1] IBM Res Corp, Zurich Res Lab, Zurich, Switzerland

[2] Natl Univ Ireland, Galway, Ireland

来源：

2007 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-7 | 2007年

关键词：

D O I：

10.1109/ISIT.2007.4557511

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

A new construction method for codes using encodings from group rings is presented. They consist primarily of two types, zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; e.g. cyclic codes are ideals in the group ring over a cyclic group. The fresh focus is on the encodings themselves, which only under very limited conditions result in ideals. Using an isomorphism between group rings and a certain well-defined ring of matrices, equivalent matrix codes are established with resulting generator and check matrices. Group rings are a fruitful source of units and zero-divisors from which new codes result. Many code properties may more easily be expressed in terms of group ring properties.

引用

页码：1981 / +

页数：2