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Further results on complete permutation monomials over finite fields
Feng, Xiutao1; Lin, Dongdai2; Wang, Liping2; Wang, Qiang3
2019-05-01
Source PublicationFINITE FIELDS AND THEIR APPLICATIONS
ISSN1071-5797
Volume57Pages:47-59
AbstractIn this paper, we construct several new classes of complete permutation monomials a(-1)x(d) over a finite field F-qn= with exponents d=q(n)-1/q-1 + 1,q(p-1)-1/q-1 + 1, and q(q-1)-1/q-1 + 1, respectively, where q = p(k) is a power of a prime number p. Our approach uses the AGW criterion (the multiplicative case) together with Dickson permutation polynomials and a class of exceptional polynomials respectively. One of our results confirms Conjecture 4.18 by G. Wu, N. Li, T. Helleseth, Y. Zhang in [42] under the assumption that the characteristic p is primitive modulo a prime number n + 1. Moreover, we show that Conjecture 4.18 is false in general using our approach and a counterexample is provided. We also reconfirm Conjecture 4.20 in [42] that was proved recently in [24], and extend some of these recent results to more general n's and more general a's. (C) 2019 Elsevier Inc. All rights reserved.
KeywordFinite fields Permutation polynomials Complete permutation polynomials Monomials
DOI10.1016/j.ffa.2019.01.003
Language英语
Funding ProjectNational Key Research and Development Program of China[2016YFB0800401] ; National Natural Science Foundation of China[61572491] ; National Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[61872355] ; NSERC of Canada[RGPIN-2017-06410]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000464301700004
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34393
Collection系统科学研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechizat, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China
3.Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada
Recommended Citation
GB/T 7714
Feng, Xiutao,Lin, Dongdai,Wang, Liping,et al. Further results on complete permutation monomials over finite fields[J]. FINITE FIELDS AND THEIR APPLICATIONS,2019,57:47-59.
APA Feng, Xiutao,Lin, Dongdai,Wang, Liping,&Wang, Qiang.(2019).Further results on complete permutation monomials over finite fields.FINITE FIELDS AND THEIR APPLICATIONS,57,47-59.
MLA Feng, Xiutao,et al."Further results on complete permutation monomials over finite fields".FINITE FIELDS AND THEIR APPLICATIONS 57(2019):47-59.
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