Volume 21, No 2, 2014, P. 52–58

UDC 519.7
N. A. Kolomeec
A threshold property of quadratic Boolean functions

Let f be a Boolean function in n variables and for any affine subspace L of dimension én/2ù  either f is affine on all shifts of L or f is not affine on any shift of L. It is proved that the algebraic degree of f can be more than 2 only if there is no affine subspace of dimension  én/2ù  that f is affine on.
Bibliogr. 8.

Keywords: Boolean function, quadratic Boolean function, bent function.

Kolomeec Nikolay Alexandrovich 1
1. Sobolev Institute of Mathematics, SB RAS,
4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
e-mail: nkolomeec@gmail.com

 © Sobolev Institute of Mathematics, 2015