Duals of non-weakly regular bent functions are not weakly regular and generalization to plateaued functions

ÖZBUDAK F., PELEN R. M.

FINITE FIELDS AND THEIR APPLICATIONS, vol.64, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 64
  • Publication Date: 2020
  • Doi Number: 10.1016/j.ffa.2020.101668
  • Journal Name: FINITE FIELDS AND THEIR APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, MathSciNet, zbMATH
  • Keywords: Non-weakly regular bent functions, Duals of bent functions, Walsh transform, Value distribution, Plateaued functions
  • Middle East Technical University Affiliated: Yes

Abstract

It is known that the dual of a weakly regular bent function is again weakly regular. On the other hand, the dual of a nonweakly regular bent function may not even be a bent function. In 2013, cesmelioglu, Meidl and Pott pointed out that the existence of a non-weakly regular bent function having weakly regular bent dual is an open problem. In this paper, we prove that for an odd prime p and n is an element of Z+, if f : F-p(n)-> F-p is a non-weakly regular bent function such that its dual f* is bent, then f**(-x) = f(x), and f* is non-weakly regular, which solves the open problem. We also generalize our results to plateaued functions. (C) 2020 Elsevier Inc. All rights reserved.