Generalized partial spreads

Abstract

We exhibit a simple condition under which the sum (modulo 2) of characteristic functions of (n/2)-dimensional vector subspaces of (GF(2))/sup n/ (n even) is a Bent function. The "Fourier" transform of such a Bent function is the sum of the characteristic functions of the duals of these spaces. The class of Bent functions that we obtain contains the whole partial spreads class. Any element of Maiorana-McFarland's class or of class D is equivalent to one of its elements. Thus this new class gives a unified insight of both general classes of Bent functions studied by Dillon (1974) in his thesis. We deduce a way to construct new classes of Bent functions and exhibit an example.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>