Geodesic
The structure of Boolean functions spectra
Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 1, pp. 57-70 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The notion of the spectrum of the Boolean function $f$ of $n$ variables is defined, its properties are investigated. The stochastic case is considered also under the assumption that the function $f$ has the uniform distribution on the set $F_n = \{f\}$ of all Boolean functions of $n$ variables. 
@article{MVK_2016_7_1_a2,
     author = {G. I. Ivchenko and Yu. I. Medvedev and V. A. Mironova},
     title = {The structure of {Boolean} functions spectra},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {57--70},
     year = {2016},
     volume = {7},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2016_7_1_a2/}
}
TY  - JOUR
AU  - G. I. Ivchenko
AU  - Yu. I. Medvedev
AU  - V. A. Mironova
TI  - The structure of Boolean functions spectra
JO  - Matematičeskie voprosy kriptografii
PY  - 2016
SP  - 57
EP  - 70
VL  - 7
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MVK_2016_7_1_a2/
LA  - ru
ID  - MVK_2016_7_1_a2
ER  - 
%0 Journal Article
%A G. I. Ivchenko
%A Yu. I. Medvedev
%A V. A. Mironova
%T The structure of Boolean functions spectra
%J Matematičeskie voprosy kriptografii
%D 2016
%P 57-70
%V 7
%N 1
%U http://geodesic.mathdoc.fr/item/MVK_2016_7_1_a2/
%G ru
%F MVK_2016_7_1_a2
G. I. Ivchenko; Yu. I. Medvedev; V. A. Mironova. The structure of Boolean functions spectra. Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 1, pp. 57-70. http://geodesic.mathdoc.fr/item/MVK_2016_7_1_a2/

[1] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, 2-e izd., MTsNMO, M., 2004, 385 pp.

[2] Glukhov M. M., Shishkov A. B., Matematicheskaya logika. Diskretnye funktsii. Teoriya algoritmov, Lan, SPb., 2012, 416 pp.

[3] Ivchenko G. I., Medvedev Yu. I., “Spektr sluchainoi bulevoi funktsii i ego proizvodyaschaya funktsiya”, Matem. voprosy kriptografii, 2:2 (2011), 41–54

[4] Tarannikov Yu. V., “O korrelyatsionno-immunnykh i ustoichivykh bulevykh funktsiyakh”, Matem. voprosy kibernetiki, ed. O. B. Lupanov, 2002, 91–148 | MR

[5] Zhang Xian-Mo, Zheng Yuliang, “GAC — the criterion for global avalanche characteristics of cryptographic functions”, J. Univ. Comput. Sci., 1:5 (1995), 320–327 | MR

[6] Canteaut A., Carlet C., Charpin P., Fontaine C., “On cryptographic properties of the cosets of $R(1, m)$”, IEEE Trans. Inform. Theory, IT-47:4 (2001), 1494–1513 | DOI | MR | Zbl

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

[8] Logachev O. A., Salnikov A. P., Yaschenko V. V., Bulevy funktsii v teorii kodirovaniya i kriptografii, 2-e izd., MTsNMO, M., 2004, 470 pp.