• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Designs, Codes and Cryptography >An intrinsical description of group codes
【24h】

An intrinsical description of group codes

机译：组码的内部描述

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

A (left) group code of length n is a linear code which is the image of a (left) ideal of a group algebra via an isomorphism mathbbFG ® mathbbFn{mathbb{F}G rightarrow mathbb{F}^n} which maps G to the standard basis of mathbbFn{mathbb{F}^n} . Many classical linear codes have been shown to be group codes. In this paper we obtain a criterion to decide when a linear code is a group code in terms of its intrinsical properties in the ambient space mathbbFn{mathbb{F}^n} , which does not assume an “a priori” group algebra structure on mathbbFn{mathbb{F}^n} . As an application we provide a family of groups (including metacyclic groups) for which every two-sided group code is an abelian group code. It is well known that Reed–Solomon codes are cyclic and its parity check extensions are elementary abelian group codes. These two classes of codes are included in the class of Cauchy codes. Using our criterion we classify the Cauchy codes of some lengths which are left group codes and the possible group code structures on these codes.
机译：长度为n的（左）组代码是线性代码，它是通过同构mathbbFG®mathbbF n {mathbb {F} G rightarrow mathbb { F} ^ n}将G映射为mathbbF n {mathbb {F} ^ n}的标准基础。已经证明许多经典的线性代码是组代码。本文根据环境空间mathbbF n {mathbb {F} ^ n}的内在属性，获得了一个判别线性代码何时为组代码的准则，该准则不假定mathbbF n {mathbb {F} ^ n}上的“先验”组代数结构。作为应用程序，我们提供了一组族（包括元环族），每个双边组代码都是一个阿贝尔群代码。众所周知，里德-所罗门码是循环的，其奇偶校验扩展是基本的阿贝尔群码。这两类代码都包含在柯西代码中。使用我们的标准，我们将一些长度的柯西码分类为左组码和这些码上可能的组码结构。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号