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

The research article “Duals of non-weakly regular bent functions are not weakly regular and generalization to plateaued functions”, co-authored by METU member Prof. Ferruh Özbudak, has been published in Finite Fields and their Applications.

It is known that the dual of a weakly regular bent function is again weakly regular. On the other hand, the dual of a non-weakly regular bent function may not even be a bent function. In 2013, Çesmelioğlu, 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∈Z+, if f:Fp n→Fp 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.

Özbudak, F., & Pelen, R. M. (2020). Duals of non-weakly regular bent functions are not weakly regular and generalization to plateaued functions. Finite Fields and their Applications, 64 doi:10.1016/j.ffa.2020.101668

Article access: https://www.sciencedirect.com/science/article/pii/S107157972030037X

Tags/Keywords:

Duals of bent functions, Non-weakly regular bent functions, Plateaued functions, Value distribution, Walsh transform

Other authors:
Pelen, R.M. (METU)