A threshold property of quadratic Boolean functions
Nikolay A. Kolomeec · Journal of Applied and Industrial Mathematics · 2015
Let f be a Boolean function of n variables such that, for every affine subspace L of dimension [ n /2], f is either affine on all shifts of L or affine on none of the shifts of L . We prove that either the degree of f is at most 2 or there is no affine subspace of dimension [ n /2] on which f is affine.