计算机工程与应用 ›› 2009, Vol. 45 ›› Issue (35): 99-100.DOI: 10.3778/j.issn.1002-8331.2009.35.030

• 网络、通信、安全 • 上一篇    下一篇

F2+uF2+u2F2上的线性码及其Gray像

梁 华1,2,唐元生2   

  1. 1.淮阴师范学院 数学系,江苏 淮安 223300
    2.扬州大学 数学科学学院,江苏 扬州225002
  • 收稿日期:2009-07-23 修回日期:2009-09-27 出版日期:2009-12-11 发布日期:2009-12-11
  • 通讯作者: 梁 华

Linear codes over F2+uF2+u2F2 and their Gray images

LIANG Hua1,2,TANG Yuan-sheng2   

  1. 1.Department of Mathematics,Huaiyin Teachers College,Huaian,Jiangsu 223300,China
    2.School of Mathematical Science,Yangzhou University,Yangzhou,Jiangsu 225002,China
  • Received:2009-07-23 Revised:2009-09-27 Online:2009-12-11 Published:2009-12-11
  • Contact: LIANG Hua

摘要: R=F2+uF2+u2F2R1=F2+uF2,定义了从RnF3n2的Gray映射Ф以及从Rn1Rn的映射f。通过对环R上线性码C的生成矩阵的研究,给出了线性码C的对偶码C和Gray像ФC)的生成矩阵,并且ФC)与ФC)是F2上的对偶码。通过映射f将环R1上的线性码与环R上的一类线性码对应起来。

Abstract: Let R=F2+uF2+u2F2 and R1=F2+uF2,the Gray map Ф from Rn to F3n2 and the map f from Rn1 to Rn are defined.By using the generator matrix of linear codes C over R,the generator matrices of the dual codes C and the Gray images ФC) of the linear codes C are given,and the linear codesФC) are the dual codes of ФC) over F2.By the map f,linear codes over R1 are correspond to a class of linear codes over R.

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