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Mat. Vopr. Kriptogr., 2014, Volume 5, Issue 3, Pages 5–15 (Mi mvk126)  

Moments of weights of random nonuniform Boolean functions

A. M. Zubkov

Steklov Mathematical Institute of RAS, Moscow

Abstract: Some nonuniform distributions on the Boolean functions of $n$ variables are considered. We obtain explicit formulas for the first two moments of the weight of Zegalkin polynomials having coefficient distributions invariant under permutations of variables (and analogous formulas for the moments of the number of monoms in the Zegalkin polynomial of Boolean function with distribution invariant under permutation of variables).

Key words: random Boolean functions, symmerical distributions, Zegalkin polynomials, mean and variance of the weight of a function.

DOI: https://doi.org/10.4213/mvk126

Full text: PDF file (706 kB)
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UDC: 519.212.2
Received 22.IV.2013

Citation: A. M. Zubkov, “Moments of weights of random nonuniform Boolean functions”, Mat. Vopr. Kriptogr., 5:3 (2014), 5–15

Citation in format AMSBIB
\Bibitem{Zub14}
\by A.~M.~Zubkov
\paper Moments of weights of random nonuniform Boolean functions
\jour Mat. Vopr. Kriptogr.
\yr 2014
\vol 5
\issue 3
\pages 5--15
\mathnet{http://mi.mathnet.ru/mvk126}
\crossref{https://doi.org/10.4213/mvk126}


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