The solution to an open problem on the bentness of Mesnager's functions
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.
|ESI Research Field|
Cited Times [WOS]:0
|Document Type||Journal Article|
|Department||Department of Computer Science and Engineering|
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
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.
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.
Tang，Chunming,et al."The solution to an open problem on the bentness of Mesnager's functions".FINITE FIELDS AND THEIR APPLICATIONS 88(2023).
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