Gray map over ring F2+uF2

doi:10.3778/j.issn.1002-8331.2010.13.015

Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (13): 51-52.DOI: 10.3778/j.issn.1002-8331.2010.13.015

• 研究、探讨 • Previous Articles Next Articles

Gray map over ring F₂+uF₂

RUI Yi-he¹，ZHU Shi-xin²

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

环F₂+uF₂上的Gray映射

芮义鹤¹，朱士信²

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

通讯作者: 芮义鹤

Abstract

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

摘要： 在有限环R=F₂+uF₂与F₂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

CLC Number:

TN911.22

RUI Yi-he¹，ZHU Shi-xin². Gray map over ring F₂+uF₂[J]. Computer Engineering and Applications, 2010, 46(13): 51-52.

芮义鹤¹，朱士信². 环F₂+uF₂上的Gray映射 [J]. 计算机工程与应用, 2010, 46(13): 51-52.

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Gray map over ring F₂+uF₂

环F₂+uF₂上的Gray映射

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