Çeşmelioğlu, AyçaMeidl, WilfriedPott, Alexander2021-05-152021-05-1520150895-48011095-7146https://doi.org/10.1137/140963273https://hdl.handle.net/20.500.12939/631We 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.eninfo:eu-repo/semantics/closedAccessBent FunctionProjective PlaneSemifieldHyperovalArticle10.1137/1409632732928548672-s2.0-84938075526Q2WOS:000357409700010Q2