Abstract
Boolean functions on the space $$\mathbb{F}_{2}^{m}$$ 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, Olejar 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 Boolean functions. This article is inspired by a paper of G. Halasz about the related problem of real polynomials with random coefficients.
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