Diskretnaya Matematika, Tome 3 (1991) no. 2, pp. 25-46
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O. V. Denisov. An asymptotic formula for the number of correlation-immune Boolean functions of order $k$. Diskretnaya Matematika, Tome 3 (1991) no. 2, pp. 25-46. http://geodesic.mathdoc.fr/item/DM_1991_3_2_a1/
@article{DM_1991_3_2_a1,
author = {O. V. Denisov},
title = {An asymptotic formula for the number of correlation-immune {Boolean} functions of order~$k$},
journal = {Diskretnaya Matematika},
pages = {25--46},
year = {1991},
volume = {3},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_1991_3_2_a1/}
}
TY - JOUR
AU - O. V. Denisov
TI - An asymptotic formula for the number of correlation-immune Boolean functions of order $k$
JO - Diskretnaya Matematika
PY - 1991
SP - 25
EP - 46
VL - 3
IS - 2
UR - http://geodesic.mathdoc.fr/item/DM_1991_3_2_a1/
LA - ru
ID - DM_1991_3_2_a1
ER -
%0 Journal Article
%A O. V. Denisov
%T An asymptotic formula for the number of correlation-immune Boolean functions of order $k$
%J Diskretnaya Matematika
%D 1991
%P 25-46
%V 3
%N 2
%U http://geodesic.mathdoc.fr/item/DM_1991_3_2_a1/
%G ru
%F DM_1991_3_2_a1
We obtain an asymptotic formula for the $N(n,k)$-number of correlation-immune Boolean $n$-variable functions of order $k$. We prove that as $n\to\infty$$$ N(n,k)\sim\frac{2^{2^n}}{2^k\exp\biggl(\sum_{i=1}^k\Bigl(\ln\sqrt\frac{\pi}2+\Bigl(\frac n2-i\Bigr)\ln2\Bigr)\binom ni\biggr)}\,, $$ where $k$ is a fixed constant that does not depend on $n$$(k=1,2,\dots$).
