Nonlinearity measures of random Boolean functions
Combinatorics
2013-08-15 v1 Information Theory
math.IT
Abstract
The r-th order nonlinearity of a Boolean function is the minimum number of elements that have to be changed in its truth table to arrive at a Boolean function of degree at most r. It is shown that the (suitably normalised) r-th order nonlinearity of a random Boolean function converges strongly for all r\ge 1. This extends results by Rodier for r=1 and by Dib for r=2. The methods in the present paper are mostly of elementary combinatorial nature and also lead to simpler proofs in the cases that r=1 or 2.
Cite
@article{arxiv.1308.3112,
title = {Nonlinearity measures of random Boolean functions},
author = {Kai-Uwe Schmidt},
journal= {arXiv preprint arXiv:1308.3112},
year = {2013}
}