On Orthomorphisms over Fn2

doi:10.13190/jbupt.200601.115.changzl

JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM ›› 2006, Vol. 29 ›› Issue (1): 115-118.doi: 10.13190/jbupt.200601.115.changzl

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On Orthomorphisms over Fⁿ₂

CHANG Zu-ling^1，2，KE Pin-hui^1，2，MO Jiao¹, WEN Qiao-yan¹

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

Abstract

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

CLC Number:

TN918.1

CHANG Zu-ling，KE Pin-hui，MO Jiao, WEN Qiao-yan. On Orthomorphisms over Fⁿ₂[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2006, 29(1): 115-118.

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On Orthomorphisms over Fⁿ₂

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