Asymptotic Nonlinearity of Boolean Functions

Boolean functions on the space Fm 2 are not only important in the theory of error-correcting codes, but also in cryptography. In these two cases, the nonlinearity of these functions is a main concept. Carlet, Olej?ar and Stanek gave an asymptotic lower bound for the nonlinearity of most of them, and I gave an asymptotic upper bound which was strictly larger. In this article, I improve the bounds and get an exact limit for the nonlinearity of most of them. This article is inspired by a paper of G. Hal?acz about the related problem of real polynomials with random coefficients.

• Type: Conference
• Year: 2006
• Where: DCC
• Authors: François Rodier
• Keywords: Asymptotic Lower Bound, Asymptotic Upper Bound, Boolean Functions, Computer Graphics, DCC 2006