Geodesic
Bounds for the number of Boolean functions admitting affine approximations of a~given accuracy
Diskretnaya Matematika, Tome 22 (2010) no. 4, pp. 3-19.

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

We obtain two-sided bounds and asymptotic formulas for the number of Boolean functions of $n$ variables which are approximated by affine or linear Boolean functions with a given accuracy. 
@article{DM_2010_22_4_a0,
     author = {A. M. Zubkov and A. A. Serov},
     title = {Bounds for the number of {Boolean} functions admitting affine approximations of a~given accuracy},
     journal = {Diskretnaya Matematika},
     pages = {3--19},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2010_22_4_a0/}
}
TY  - JOUR
AU  - A. M. Zubkov
AU  - A. A. Serov
TI  - Bounds for the number of Boolean functions admitting affine approximations of a~given accuracy
JO  - Diskretnaya Matematika
PY  - 2010
SP  - 3
EP  - 19
VL  - 22
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2010_22_4_a0/
LA  - ru
ID  - DM_2010_22_4_a0
ER  - 
%0 Journal Article
%A A. M. Zubkov
%A A. A. Serov
%T Bounds for the number of Boolean functions admitting affine approximations of a~given accuracy
%J Diskretnaya Matematika
%D 2010
%P 3-19
%V 22
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2010_22_4_a0/
%G ru
%F DM_2010_22_4_a0
A. M. Zubkov; A. A. Serov. Bounds for the number of Boolean functions admitting affine approximations of a~given accuracy. Diskretnaya Matematika, Tome 22 (2010) no. 4, pp. 3-19. http://geodesic.mathdoc.fr/item/DM_2010_22_4_a0/

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

[2] Ryazanov B. V., “Probabilistic methods in the theory of approximation of discrete functions”, Probabilistic Methods of Discrete Mathematics, TVP/VSP, Moscow, 1993, 403–412 | MR | Zbl

[3] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 1, Mir, Moskva, 1984 | Zbl

[4] Checheta S. I., “O predelnom raspredelenii rasstoyaniya mezhdu sluchainym vektorom i nekotorymi dvoichnymi kodami”, Problemy peredachi informatsii, 31:1 (1995), 90–98 | Zbl

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

[6] Alfers D., Dinges H., “A normal approximation for Beta and Gamma tail probabilities”, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 65 (1984), 399–420 | DOI | MR | Zbl