Geodesic
Analysis of the spectrum of random symmetric Boolean functions
Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 1, pp. 59-76 
G. I. Ivchenko; Yu. I. Medvedev; V. A. Mironova. Analysis of the spectrum of random symmetric Boolean functions. Matematičeskie voprosy kriptografii, Tome 4 (2013) no. 1, pp. 59-76. http://geodesic.mathdoc.fr/item/MVK_2013_4_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

General probabilistic model of a random symmetric Boolean function of $n$ variables is proposed. The characteristic function of the Walsh spectrum of a random symmetric Boolean function is defined; exact and asymptotic distributions of some spectrum characteristics as $n\to\infty$ are obtained in the case of the parametric measure. The basic properties of the Krawtchouk's polynomials (which are used in proofs) are reviewed.

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