Geodesic
A local limit theorem for the distribution of a part of the spectrum of a random binary function
Diskretnaya Matematika, Tome 12 (2000) no. 1, pp. 82-95.

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

We obtain a local limit theorem for the distribution of the vector (of growing dimension) consisting of some spectral coefficients of a random binary function of $n$ variables as $n\to\infty$. We correct a mistake in the asymptotic formula for the number of correlation-immune functions of order $k$ obtained in previous author's paper. We prove an asymptotic formula for the number of $(n,1,k)$-resilient functions as $n\to\infty$ and $k=k(n)=o(\sqrt n)$. 
@article{DM_2000_12_1_a6,
     author = {O. V. Denisov},
     title = {A local limit theorem for the distribution of a part of the spectrum of a random binary function},
     journal = {Diskretnaya Matematika},
     pages = {82--95},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2000_12_1_a6/}
}
TY  - JOUR
AU  - O. V. Denisov
TI  - A local limit theorem for the distribution of a part of the spectrum of a random binary function
JO  - Diskretnaya Matematika
PY  - 2000
SP  - 82
EP  - 95
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2000_12_1_a6/
LA  - ru
ID  - DM_2000_12_1_a6
ER  - 
%0 Journal Article
%A O. V. Denisov
%T A local limit theorem for the distribution of a part of the spectrum of a random binary function
%J Diskretnaya Matematika
%D 2000
%P 82-95
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2000_12_1_a6/
%G ru
%F DM_2000_12_1_a6
O. V. Denisov. A local limit theorem for the distribution of a part of the spectrum of a random binary function. Diskretnaya Matematika, Tome 12 (2000) no. 1, pp. 82-95. http://geodesic.mathdoc.fr/item/DM_2000_12_1_a6/

[1] Denisov O. V., “Asimptoticheskaya formula dlya chisla korrelyatsionno-immunnykh poryadka $k$ bulevykh funktsii”, Diskretnaya matematika, 3:2 (1991), 25–46 | MR

[2] Zuev Yu. A., “Kombinatorno-veroyatnostnye i geometricheskie metody v porogovoi logike”, Diskretnaya matematika, 3:2 (1991), 47–57 | MR

[3] Kuznetsov Yu. V., Shkarin S. A., Matem. voprosy kibernetiki, 1996, no. 6, Kody Rida–Mallera (obzor publikatsii)

[4] Ryazanov B. V., “O raspredelenii spektralnoi slozhnosti bulevykh funktsii”, Diskretnaya matematika, 6:2 (1994), 111–129 | MR

[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] Chow C. K., “On the characterization of threshold functions”, Minimization of Boolean Functions and Logical Design. Switching Circuit Theory and Logical Design (AIEE Special Publication), 134, 1961, 34–38

[7] Guo-Zhen X., Massey J. L., “A spectral characterization of correlation-immune combining functions”, IEEE Trans. Information Theory, 34, 1988, 569–571 | MR | Zbl

[8] Gopalakrishnan K., Stinson D. R., “Three characterization of non-binary correlation-immune and resilient functions”, Designs, Codes and Cryptography, 5 (1995), 241–251 | DOI | MR | Zbl