Explicit constructions of bent functions from pseudo-planar functions

We investigate explicit constructions of bent functions which are linear on elements of spreads. Our constructions are obtained from symplectic presemifields which are associated to pseudo-planar functions. The following diagram gives an indication of the main interconnections arising in this paper: \begin{document} $pseudo-planar\ functions \longleftrightarrow\ commutaive\ presemifields \longrightarrow bent\ functions$ \end{document}