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Stochastic Boolean functions and their spectra
Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 3, pp. 21-34 Cet article a éte moissonné depuis la source Math-Net.Ru

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General probabilistic model for Boolean functions of $n$ variables with arbitrary probabilistic measure on the set of such functions is proposed. The characteristic function of Walsh spectrum of random function is defined and exact and asymptotic distributions of some spectrum characteristics for $n\to\infty$ are obtained in the parametric measure case. 
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     author = {G. I. Ivchenko and Yu. I. Medvedev},
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G. I. Ivchenko; Yu. I. Medvedev. Stochastic Boolean functions and their spectra. Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 3, pp. 21-34. http://geodesic.mathdoc.fr/item/MVK_2012_3_3_a1/

[1] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, 2-e izd., MTsNMO, M., 2004

[2] Logachëv O. A., Salnikov A. L., Yaschenko V. V., Bulevy funktsii v teorii kodirovaniya i kriptologii, MTsNMO, M., 2004

[3] Cusick Th. W., Stanica P., Cryptographic Boolean functions and applications, AP Elsevier, Amsterdam etc., 2009 | MR | Zbl

[4] Ivchenko G. I., Medvedev Yu. I., “Spektr sluchainoi bulevoi funktsii i ego proizvodyaschaya funktsiya”, Matematicheskie voprosy kriptografii, 2:2 (2011), 41–53

[5] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 2, Mir, M., 1984 | MR | Zbl