南方科技大学知识苑(SUSTech KC): The solution to an open problem on the bentness of Mesnager's functions

题名	The solution to an open problem on the bentness of Mesnager's functions
作者	Tang，Chunming 1; Han，Peng 2; Wang，Qi3 ; Zhang，Jun 4; Qi，Yanfeng 5
通讯作者	Tang，Chunming
发表日期	2023-06-01
DOI	10.1016/j.ffa.2023.102170
发表期刊	FINITE FIELDS AND THEIR APPLICATIONS 影响因子和分区
ISSN	1071-5797
EISSN	1090-2465
卷号	88
摘要	Let n=2m. In the present paper, we study the binomial Boolean functions of the form [Formula presented] where m is an even positive integer, a∈F and b∈F. We show that f is a bent function if the Kloosterman sum [Formula presented] equals 4, thus settling an open problem of Mesnager. The proof employs tools including computing Walsh coefficients of Boolean functions via multiplicative characters, divisibility properties of Gauss sums, and graph theory.
关键词	Bent function Boolean function Directed graph Gauss sum Walsh transform
相关链接	[Scopus记录]
收录类别	SCI ; EI
语种	英语
学校署名	其他
WOS记录号	WOS:000964670000001
EI入藏号	20230813617517
EI主题词	Directed graphs ; Walsh transforms
EI分类号	Computer Theory, Includes Formal Logic, Automata Theory, Switching Theory, Programming Theory:721.1 ; Algebra:921.1 ; Mathematical Transformations:921.3 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4
ESI学科分类	MATHEMATICS
Scopus记录号	2-s2.0-85148331811
来源库	Scopus
引用统计	被引频次[WOS]：0
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/489736
专题	工学院_计算机科学与工程系
作者单位	1.School of Information Science and Technology,Southwest Jiaotong University,Chengdu,610031,China 2.School of Mathematics and Information,China West Normal University,Nanchong,Sichuan,637002,China 3.Department of Computer Science and Engineering,Southern University of Science and Technology,Shenzhen,518055,China 4.School of Mathematical Sciences,Capital Normal University,Beijing,100048,China 5.School of Science,Hangzhou Dianzi University,Hangzhou,Zhejiang,310018,China
推荐引用方式 GB/T 7714	Tang，Chunming,Han，Peng,Wang，Qi,et al. The solution to an open problem on the bentness of Mesnager's functions[J]. FINITE FIELDS AND THEIR APPLICATIONS,2023,88.
APA	Tang，Chunming,Han，Peng,Wang，Qi,Zhang，Jun,&Qi，Yanfeng.(2023).The solution to an open problem on the bentness of Mesnager's functions.FINITE FIELDS AND THEIR APPLICATIONS,88.
MLA	Tang，Chunming,et al."The solution to an open problem on the bentness of Mesnager's functions".FINITE FIELDS AND THEIR APPLICATIONS 88(2023).