Claude Carlet
GREYC, Université de Caen
and
INRIA, projet CODES
BP 105
78153 Le Chesnay Cedex, France Claude.Carlet@inria.fr

IEEE Transactions on Information Theory, 41(5): 1482-1487, 1995.

Abstract

We exhibit a simple condition under which the sum (modulo 2) of
characteristic functions of n/2 - dimensional vector-subspaces of
GF(2)^{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 J.F. Dillon in his thesis. We
deduce a way to construct new classes of bent functions and exhibit an
example.