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Dembowski-Ostrom polynomials from reversed Dickson polynomials
Zhang Xiaoming1; Wu Baofeng1,2; Liu Zhuojun1
2016-02-01
Source PublicationJOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN1009-6124
Volume29Issue:1Pages:259-271
AbstractThis paper gives a full classification of Dembowski-Ostrom polynomials derived from the compositions of reversed Dickson polynomials and monomials over finite fields of characteristic 2. The authors also classify almost perfect nonlinear functions among all such Dembowski-Ostrom polynomials based on a general result describing when the composition of an arbitrary linearized polynomial and a monomial of the form is almost perfect nonlinear. It turns out that almost perfect nonlinear functions derived from reversed Dickson polynomials are all extended affine equivalent to the well-known Gold functions.
KeywordAlmost perfect nonlinear function Dembowski-Ostrom polynomial linearized polynomial reversed Dickson polynomial
DOI10.1007/s11424-015-4110-4
Language英语
Funding ProjectNational Basic Research Program of China[2011CB302400]
WOS Research AreaMathematics
WOS SubjectMathematics, Interdisciplinary Applications
WOS IDWOS:000370162300016
PublisherSPRINGER HEIDELBERG
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/22031
Collection系统科学研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China
Recommended Citation
GB/T 7714
Zhang Xiaoming,Wu Baofeng,Liu Zhuojun. Dembowski-Ostrom polynomials from reversed Dickson polynomials[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2016,29(1):259-271.
APA Zhang Xiaoming,Wu Baofeng,&Liu Zhuojun.(2016).Dembowski-Ostrom polynomials from reversed Dickson polynomials.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,29(1),259-271.
MLA Zhang Xiaoming,et al."Dembowski-Ostrom polynomials from reversed Dickson polynomials".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 29.1(2016):259-271.
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