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

Date

2020-06-01

Author

Özbudak, Ferruh

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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.

Subject Keywords

Theoretical Computer Science, General Engineering, Algebra and Number Theory, Applied Mathematics, Non-weakly regular bent functions, Duals of bent functions, Walsh transform, Value distribution, Plateaued functions

URI

https://hdl.handle.net/11511/34526

Journal

FINITE FIELDS AND THEIR APPLICATIONS

DOI

https://doi.org/10.1016/j.ffa.2020.101668

Collections

Department of Mathematics, Article

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Citation Formats

F. Özbudak, “Duals of non-weakly regular bent functions are not weakly regular and generalization to plateaued functions,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 0–0, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34526.