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Diskretnyi Analiz i Issledovanie Operatsii, 2014, Volume 21, Issue 2, Pages 52–58
(Mi da766)
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This article is cited in 2 scientific papers (total in 2 papers)
A threshold property of quadratic Boolean functions
N. A. Kolomeec S. L. Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
Abstract:
Let $f$ be a Boolean function in $n$ variables and for any affine subspace $L$ of dimension $\lceil n/2\rceil$ either $f$ is affine on all shifts of $L$ or $f$ is not affine on any shift of $L$. It is proved that the algebraic degree of $f$ can be more than 2 only if there is no affine subspace of dimension $\lceil n/2\rceil$ that $f$ is affine on. Bibliogr. 8.
Keywords:
Boolean function, quadratic Boolean function, bent function.
Received: 09.07.2013 Revised: 24.12.2013
Citation:
N. A. Kolomeec, “A threshold property of quadratic Boolean functions”, Diskretn. Anal. Issled. Oper., 21:2 (2014), 52–58; J. Appl. Industr. Math., 9:1 (2015), 83–87
Linking options:
https://www.mathnet.ru/eng/da766 https://www.mathnet.ru/eng/da/v21/i2/p52
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Abstract page: | 297 | Full-text PDF : | 102 | References: | 46 | First page: | 9 |
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