Bent functions, spreads, and o-polynomials
[ X ]
Tarih
2015
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Siam Publications
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
We show that bent functions f from F(p)m x F(p)m to F-p, which are constant or affine on the elements of a given spread of F(p)m x F(p)m, either arise from partial spread bent functions, or they are Boolean and a generalization of Dillon's class H. For spreads of a presemifield S, we show that a bent function of the second class corresponds to an o-polynomial of a presemifield in the Knuth orbit of S. In contrast to the finite fields case, we have to consider pairs of (pre) semifields in a Knuth orbit. We give a canonical example of an o-polynomial for commutative presemifields (which also defines a hyperoval on the semifield plane) and show that the corresponding bent functions belong to the completed Maiorana-McFarland class. Using Albert's twisted fields and Kantor's family of presemifields, we explicitly present examples of such bent functions.
Açıklama
Anahtar Kelimeler
Bent Function, Projective Plane, Semifield, Hyperoval
Kaynak
Siam Journal on Discrete Mathematics
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
Cilt
29
Sayı
2
