计算机工程与应用 ›› 2010, Vol. 46 ›› Issue (13): 51-52.DOI: 10.3778/j.issn.1002-8331.2010.13.015

• 研究、探讨 • 上一篇    下一篇

F2+uF2上的Gray映射

芮义鹤1,朱士信2   

  1. 1.浙江工商大学 统计与数学学院,杭州 310018
    2.合肥工业大学 数学系,合肥 230009
  • 收稿日期:2009-10-26 修回日期:2010-02-04 出版日期:2010-05-01 发布日期:2010-05-01
  • 通讯作者: 芮义鹤

Gray map over ring F2+uF2

RUI Yi-he1,ZHU Shi-xin2   

  1. 1.College of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China
    2.Department of Mathematics,Hefei University of Technology,Hefei 230009,China
  • Received:2009-10-26 Revised:2010-02-04 Online:2010-05-01 Published:2010-05-01
  • Contact: RUI Yi-he

摘要: 在有限环R=F2+uF2F2之间定义了一个新的Gray映射。证明了该映射是(Rn,Lee重量)到(F2n,Hamming重量)的等重等距映射,同时证明了环F2+uF2上线性码C的二元像Φ(C)是距离不变码,而且如果环F2+uF2上线性码C是Lee恒距码,则二元像Φ(C)是F2上Hamming恒距码。

关键词: 线性码, Gray映射, Lee重量, Hamming重量, 恒距码

Abstract: In this paper,the Gray map ?准 form R=F2+uF2 to F2 is given,and the Gray map is proved to be weight-preserving and distance-preserving.The binary image of a linear code C over ring R,called Φ(C) is Hamming distance invariant,if C is Lee distance invariant.

Key words: linear code, Gray map, Lee weight, Hamming weight, distance invariant code

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