Further results on complete permutation monomials over finite fields

doi:10.1016/j.ffa.2019.01.003

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	Further results on complete permutation monomials over finite fields
	Feng, Xiutao2 ; Lin, Dongdai 1; Wang, Liping 1; Wang, Qiang 3
刊名	FINITE FIELDS AND THEIR APPLICATIONS
	2019-05-01
卷号	57 页码:47-59
关键词	Finite fields Permutation polynomials Complete permutation polynomials Monomials
ISSN号	1071-5797
DOI	10.1016/j.ffa.2019.01.003
英文摘要	In 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.
资助项目	National 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研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000464301700004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/34392]
专题	系统科学研究所
通讯作者	Wang, Qiang
作者单位	1.Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechizat, Beijing 100190, Peoples R China 3.Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada
推荐引用方式 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.