Enumeration of Boolean functions with a~fixed number of affine products
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 43-47.

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

A recursive enumeration method for determining the number of Boolean functions with a fixed number of affine products and fixed function weights or nonlinearity degree is proposed.
Keywords: Boolean function
Mots-clés : affine classification, Möbius inversion.
@article{PDMA_2015_8_a16,
     author = {A. V. Cheremushkin},
     title = {Enumeration of {Boolean} functions with a~fixed number of affine products},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {43--47},
     publisher = {mathdoc},
     number = {8},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2015_8_a16/}
}
TY  - JOUR
AU  - A. V. Cheremushkin
TI  - Enumeration of Boolean functions with a~fixed number of affine products
JO  - Prikladnaya Diskretnaya Matematika. Supplement
PY  - 2015
SP  - 43
EP  - 47
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDMA_2015_8_a16/
LA  - ru
ID  - PDMA_2015_8_a16
ER  - 
%0 Journal Article
%A A. V. Cheremushkin
%T Enumeration of Boolean functions with a~fixed number of affine products
%J Prikladnaya Diskretnaya Matematika. Supplement
%D 2015
%P 43-47
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDMA_2015_8_a16/
%G ru
%F PDMA_2015_8_a16
A. V. Cheremushkin. Enumeration of Boolean functions with a~fixed number of affine products. Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 43-47. http://geodesic.mathdoc.fr/item/PDMA_2015_8_a16/

[1] Comtet M. L., “Nombres de Stirling generaux et fonctions symmetriques”, C. R. Acad. Sc. Paris Ser. A., 275 (1972), 747–750 | MR | Zbl

[2] Bender E. A., Goldman J. R., “On the application of the Möbius inversion in combinatorial analysis”, Amer. Math. Monthly, 82:8 (1975), 789–803 | DOI | MR | Zbl

[3] Cheremushkin A. V., “Metody affinnoi i lineinoi klassifikatsii dvoichnykh funktsii”, Trudy po diskretnoi matematike, 4, Fizmatlit, M., 2001, 273–314

[4] Tu Z., Deng Y., Algebraic Immunity Hierarchy of Boolean Functions, Cryptology ePrint Archive, Report 2007/259, , 2007, 6 pp. http://eprint.iacr.org/2007/259