Geodesic
Mean and variance of the number of subfunctions of random Boolean function which are close to the affine functions set} \runningtitle{Mean and variance of the number of subfunctions of random Boolean function
Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 108-122.

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

For random equiprobable Boolean functions we investigate the distribution of the number of subfunctions which have a given number of variables and are close to the set of affine Boolean functions. It is shown, for example, that for Boolean functions of $n$ variables the mean number of subfunctions having $ s \geqslant 3+ \log_2 n $ variables and the Hamming distance to the set of affine functions smaller than $ 2 ^ {s-2} $ tends to $ 0 $ as $ n \rightarrow \infty $.
Keywords: random Boolean function, subfunction, affine Boolean functions, Hamming distance. 
@article{DM_2015_27_3_a7,
     author = {A. A. Serov},
     title = {Mean and variance of the number of subfunctions of random {Boolean} function which are close to the affine functions set} {\runningtitle{Mean} and variance of the number of subfunctions of random {Boolean} function},
     journal = {Diskretnaya Matematika},
     pages = {108--122},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_3_a7/}
}
TY  - JOUR
AU  - A. A. Serov
TI  - Mean and variance of the number of subfunctions of random Boolean function which are close to the affine functions set} \runningtitle{Mean and variance of the number of subfunctions of random Boolean function
JO  - Diskretnaya Matematika
PY  - 2015
SP  - 108
EP  - 122
VL  - 27
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2015_27_3_a7/
LA  - ru
ID  - DM_2015_27_3_a7
ER  - 
%0 Journal Article
%A A. A. Serov
%T Mean and variance of the number of subfunctions of random Boolean function which are close to the affine functions set} \runningtitle{Mean and variance of the number of subfunctions of random Boolean function
%J Diskretnaya Matematika
%D 2015
%P 108-122
%V 27
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2015_27_3_a7/
%G ru
%F DM_2015_27_3_a7
A. A. Serov. Mean and variance of the number of subfunctions of random Boolean function which are close to the affine functions set} \runningtitle{Mean and variance of the number of subfunctions of random Boolean function. Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 108-122. http://geodesic.mathdoc.fr/item/DM_2015_27_3_a7/

[1] Zubkov A. M., Serov A. A., “Otsenka chisla bulevykh funktsii, imeyuschikh affinnye priblizheniya zadannoi tochnosti”, Diskret. matem., 22:4 (2010), 3–19 | DOI | MR | Zbl

[2] Serov A.A., “Otsenka chisla bulevykh funktsii, imeyuschikh kvadratichnye priblizheniya zadannoi tochnosti”, Diskret. matem., 24:3 (2012), 90–107 | DOI | MR | Zbl

[3] Zubkov A. M., Serov A. A., “Polnoe dokazatelstvo universalnykh neravenstv dlya funktsii raspredeleniya binomialnogo zakona”, Teoriya veroyatn. i ee primen., 57:3 (2012), 597–602 | DOI | MR

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

[5] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 1, Mir, M., 1984