Geodesic
Moments of weights of random nonuniform Boolean functions
Matematičeskie voprosy kriptografii, Tome 5 (2014) no. 3, pp. 5-15 Cet article a éte moissonné depuis la source Math-Net.Ru

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Some nonuniform distributions on the Boolean functions of $n$ variables are considered. We obtain explicit formulas for the first two moments of the weight of Zegalkin polynomials having coefficient distributions invariant under permutations of variables (and analogous formulas for the moments of the number of monoms in the Zegalkin polynomial of Boolean function with distribution invariant under permutation of variables). 
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A. M. Zubkov. Moments of weights of random nonuniform Boolean functions. Matematičeskie voprosy kriptografii, Tome 5 (2014) no. 3, pp. 5-15. http://geodesic.mathdoc.fr/item/MVK_2014_5_3_a0/

[1] Gardy D., Woods A., “And/or tree probabilities of Boolean functions”, 2005 Intern. Conf. Analysis of Algorithms, DMTCS Proceedings, AD, 2005, 139–146 | MR | Zbl

[2] Genitrini A., Gittenberger B., “No Shannon effect on probability distributions on Boolean functions induced by Boolean expressions”, Proc. of Analysis of Algorithms, Wien, Austria, 2010, 303–316 | MR

[3] Lefmann H., Savicky P., “Some typical properties of large and/or Boolean formulas”, Random Struct. Algor., 10 (1997), 337–351 | 3.0.CO;2-X class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | 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] Ivchenko G. I., Medvedev Yu. I., “Stokhasticheskie bulevy funktsii i ikh spektry”, Matematicheskie voprosy kriptografii, 3:3 (2013), 21–34

[6] Ivchenko G. I., Medvedev Yu. I., Mironova V. A., “Analiz spektra simmetricheskikh bulevykh funktsii”, Matematicheskie voprosy kriptografii, 4:1 (2013), 59–76

[7] Ivchenko G. I., Medvedev Yu. I., Mironova V. A., “Simmetricheskie bulevy funktsii i ikh metricheskie svoistva”, Matematicheskie voprosy kriptografii, 4:4 (2013), 49–63

[8] Logachev O. A., Salnikov A. A., Yaschenko V. V., Bulevy funktsii v teorii kodirovaniya i kriptologii, MTsNMO, M., 2004