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Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei

6 Issues per year


CiteScore 2016: 0.16

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.552

Online
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1569-3929
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Volume 27, Issue 1 (Feb 2017)

Issues

Mean and variance of the number of subfunctions of random Boolean function which are close to the affine functions set

Aleksandr A. Serov
Published Online: 2017-03-20 | DOI: https://doi.org/10.1515/dma-2017-0004

Abstract

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 ⩾ 3 + log2n variables and the Hamming distance to the set of affine functions smaller than 2s−2 tends to 0 as n → ∞.

Keywords: random Boolean function; subfunction; affine Boolean functions; Hamming distance

Originally published in Diskretnaya Matematika (2015) 27, N-o 3, 108–122 (in Russian).

References

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    Zubkov A. M., Serov A. A., “Bounds for the number of Boolean functions admitting affine approximations of a given accuracy”, Discrete Math. Appi., 20:5-6 (2010), 467–486.Google Scholar

  • [2]

    Serov A. A., “Bounds for the number of Boolean functions admitting quadratic approximations of given accuracy”, Discrete Math. Appi., 22:4 (2012), 455–475.Google Scholar

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    Zubkov A. M., Serov A. A., “A complete proof of universal inequalities for distribution function of binomial law”, Theory Probab. Appi, 57:3 (2013), 539–544.Google Scholar

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    Logachev O. A., Sal’nikov A. A., Yashchenko V. V., Boolean functions in coding theory and cryptology, MCCME, Moscow, 2004 (in Russian).Google Scholar

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    Feller W., An Introduction to Probability Theory and Its Applications. V. 1,3rd edition, Wiley, 1968,528 pp.Google Scholar

About the article

Received: 2015-02-17

Published Online: 2017-03-20

Published in Print: 2017-02-01


Citation Information: Discrete Mathematics and Applications, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265, DOI: https://doi.org/10.1515/dma-2017-0004.

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