北京邮电大学学报

  • EI核心期刊

北京邮电大学学报 ›› 2006, Vol. 29 ›› Issue (1): 115-118.doi: 10.13190/jbupt.200601.115.changzl

• 研究报告 • 上一篇    下一篇

Fn2上的正形置换

常祖领1,2,柯品惠1,2,莫 骄1,温巧燕1   

  1. 1.北京邮电大学 理学院, 北京 100876
    2.中国科学院 信息安全国家重点实验室,  北京 100039
  • 收稿日期:2004-12-07 出版日期:2006-02-28 发布日期:2006-02-28
  • 通讯作者: 常祖领 E-mail:zlchang@eyou.com
  • 作者简介:常祖领(1976—),男,博士后,E-mail: zlchang@eyou.com.
  • 基金资助:

    国家自然科学基金项目(60373059); 教育部博士点基金项目(20040013007); 中科院信息安全重点实验室开放基金项目

On Orthomorphisms over Fn2

CHANG Zu-ling1,2,KE Pin-hui1,2,MO Jiao1, WEN Qiao-yan1   

  1. 1.School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China
    2.State Key Laboratory of Information Security, Chinese Academy of Sciences, Beijing 100039, China
  • Received:2004-12-07 Online:2006-02-28 Published:2006-02-28
  • Contact: CHANG Zu-ling E-mail:zlchang@eyou.com

摘要:

讨论了正形置换的构造和性质,并分析了正形置换的幂次是否仍是正形置换. 对于线性正形置换, 根据矩阵标准型的性质,只要整数i不能被这个正形置换对应矩阵的极小多项式的各个根的阶整除,则这个线性正形置换的i次幂仍是线性正形置换. 对于非线性正形置换,给出了有用的结果.

关键词: 置换, 正形置换, 若当标准型

Abstract:

We mainly discuss the constructions and properties of orthomorphisms, and concern whether the power of one orthomorphism is still one orthomorphism. For linear orthomorphism, using the properties of canonical form of matrix, if integer i can't be divided exactly by the orders of roots of the minimum polynomial of the matrix corresponding to this orthomorphism, then the i-th power of this linear orthomorphism is still one linear orthomorphism. For nonlinear orthomophisms, we provide some useful results.

Key words: permutations, orthomorphisms, jordan canonical form

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