Son Güncelleme:

21/08/2020 - 16:43

Üniversitemiz öğretim üyelerinden Prof. Dr. Ferruh Özbudak’ın yazarları arasında bulunduğu “Duals of non-weakly regular bent functions are not weakly regular and generalization to plateaued functions” başlıklı makale Finite Fields and their Applications’ta yayınlandı.

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

 

Makaleye erişim için: https://www.sciencedirect.com/science/article/pii/S107157972030037X


ODTÜ Yazarı

Prof. Ferruh Özbudak

ozbudak@metu.edu.tr Scopus Yazar Kimliği: 6603589033
Yazar Hakkında ORCID: 0000-0002-1694-9283

Etiketler/Anahtar sözcükler:

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


Diğer Yazarlar:
Pelen, R.M. (ODTÜ)