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Prikladnaya Diskretnaya Matematika, 2008, Number 1(1), Pages 10–14
(Mi pdm3)
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This article is cited in 2 scientific papers (total in 2 papers)
Theoretical Foundations of Applied Discrete Mathematics
Approximation of plateaued boolean functions by monomial ones
A. V. Ivanov Moscow State Institute of Radio-Engineering, Electronics and Automation
Abstract:
From the Parseval's equation we have that if the squared Walsh transform of the Boolean function takes at most one nonzero value then its Walsh coefficients are equal to $2^{2n-2s}$ for some $s\le n/2$. These functions are called the $2s$-order plateaued functions. In the present paper we consider the aspects of an approximation of the plateaued functions by monomial ones. We use the representation of $n$-variable Boolean functions by polynomials over the field $\mathbb F_{2^n}$. The necessary conditions for the Boolean functions to have the Hamming distance to all bijective monomials taking only three values: $2^{n-1}$, $2^{n-1}\pm 2^{n-s-1}$, are obtained. The non-existence of the functions, satisfying these conditions for such $n$ that $2^n-1$ is prime, is shown.
Citation:
A. V. Ivanov, “Approximation of plateaued boolean functions by monomial ones”, Prikl. Diskr. Mat., 2008, no. 1(1), 10–14
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https://www.mathnet.ru/eng/pdm3 https://www.mathnet.ru/eng/pdm/y2008/i1/p10
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Abstract page: | 370 | Full-text PDF : | 118 | First page: | 2 |
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