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, Xiutao1 ; Lin, Dongdai 2; Wang, Liping 2; Wang, Qiang 3
	2019-05-01
发表期刊	FINITE FIELDS AND THEIR APPLICATIONS
ISSN	1071-5797
卷号	57 页码:47-59
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.
关键词	Finite fields Permutation polynomials Complete permutation polynomials Monomials
DOI	10.1016/j.ffa.2019.01.003
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000464301700004
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34393
专题	系统科学研究所
通讯作者	Wang, Qiang
作者单位	1.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
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.