2024/11/24 by Ziran Tu, Sihem Mesnager, Tu, Ziran +8
Mathematics · #Differential Equations and Boundary Problems #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Functional Equations Stability Results #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2411.15750
openalex publication_date 2024/11/24 · openalex created_date 2024/12/04 · openalex updated_date 2026/07/28
Dillon-like Boolean functions are known, in the literature, to be those trace polynomial functions from \mathbbF22n to \mathbbF2, with all the exponents being multiples of 2n-1 often called Dillon-like exponents. This paper is devoted to bent functions in which we study the bentness of some classes of Dillon-like Boolean functions connected with rational trace functions. Specifically, we introduce a special infinite family of trace rational functions. We shall use these functions as building blocks and generalise notably a criterion due to Li et al. published in [IEEE Trans. Inf. Theory 59(3), pp. 1818-1831, 2013] on the bentness of Dillon-like functions in the binary case, we explicitly characterize three classes of bent functions. These characterizations are expressed in terms of the well-known binary Kloosterman sums. Furthermore, analysis and experiments indicate that new functions not EA-equivalent to all known classes of monomial functions are included in our classes.