Geodesic
Spectrum of random Boolean function and its generating function
Matematičeskie voprosy kriptografii, Tome 2 (2011) no. 2, pp. 41-53 Cet article a éte moissonné depuis la source Math-Net.Ru

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Properties of spectrum of random Boolean function of $n$ variables are investigated. Joint generating function of spectrum elements is defined and exact and asymptotic distributions of some spectrum characteristics for $n\to\infty$ are obtained. 
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G. I. Ivchenko; Yu. I. Medvedev. Spectrum of random Boolean function and its generating function. Matematičeskie voprosy kriptografii, Tome 2 (2011) no. 2, pp. 41-53. http://geodesic.mathdoc.fr/item/MVK_2011_2_2_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 | Zbl

[4] Tarannikov Yu. V., “O korrelyatsionno-immunnykh i ustoichivykh bulevykh funktsiyakh”, Matematicheskie voprosy kibernetiki, 11, 2002, 91–148 | Zbl

[5] Kuznetsov Yu. V., Shkarin S. A., “Kody Rida-Mallera (obzor publikatsii)”, Matematicheskie voprosy kibernetiki, 6, 1996, 120–137

[6] Ryazanov B. V., “O raspredelenii spektralnoi slozhnosti bulevykh funktsii”, Diskretn. matem., 6:2 (1994), 111–119 | MR | Zbl

[7] Ryazanov B. V., Chechëta S. I., “O priblizhenii sluchainoi bulevoi funktsii mnozhestvom kvadratichnykh form”, Diskretn. matem., 7:3 (1995), 129–145 | MR | Zbl

[8] Denisov O. V., “Lokalnaya predelnaya teorema dlya raspredeleniya chasti spektra sluchainoi dvoichnoi funktsii”, Diskretn. matem., 12:1 (2000), 82–95 | MR | Zbl