Geodesic
Stochastic Boolean functions and their spectra
Matematičeskie voprosy kriptografii, Tome 3 (2012) no. 3, pp. 21-34 
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/
@article{MVK_2012_3_3_a1,
     author = {G. I. Ivchenko and Yu. I. Medvedev},
     title = {Stochastic {Boolean} functions and their spectra},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {21--34},
     year = {2012},
     volume = {3},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2012_3_3_a1/}
}
TY  - JOUR
AU  - G. I. Ivchenko
AU  - Yu. I. Medvedev
TI  - Stochastic Boolean functions and their spectra
JO  - Matematičeskie voprosy kriptografii
PY  - 2012
SP  - 21
EP  - 34
VL  - 3
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MVK_2012_3_3_a1/
LA  - ru
ID  - MVK_2012_3_3_a1
ER  - 
%0 Journal Article
%A G. I. Ivchenko
%A Yu. I. Medvedev
%T Stochastic Boolean functions and their spectra
%J Matematičeskie voprosy kriptografii
%D 2012
%P 21-34
%V 3
%N 3
%U http://geodesic.mathdoc.fr/item/MVK_2012_3_3_a1/
%G ru
%F MVK_2012_3_3_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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