Abstract:
We obtain achievable lower and upper bounds for the sums of modules of Walsh coefficients of Boolean functions of n variables. An average value of such sums in the class of all Boolean functions of n variables and in its subclass consisting of all balanced functions is evaluated. We present some classes of nonlinear balanced functions whose sums of modules of Walsh coefficients are close to the obtained lower and upper bounds.
Citation:
R. A. De La Krus Khimenes, O. V. Kamlovskii, “The sum of modules of Walsh coefficients of Boolean functions”, Diskr. Mat., 27:4 (2015), 49–66; Discrete Math. Appl., 26:5 (2016), 259–272
\Bibitem{De Kam15}
\by R.~A.~De La Krus Khimenes, O.~V.~Kamlovskii
\paper The sum of modules of Walsh coefficients of Boolean functions
\jour Diskr. Mat.
\yr 2015
\vol 27
\issue 4
\pages 49--66
\mathnet{http://mi.mathnet.ru/dm1347}
\crossref{https://doi.org/10.4213/dm1347}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3497372}
\elib{https://elibrary.ru/item.asp?id=24849940}
\transl
\jour Discrete Math. Appl.
\yr 2016
\vol 26
\issue 5
\pages 259--272
\crossref{https://doi.org/10.1515/dma-2016-0023}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000390939400002}
Linking options:
https://www.mathnet.ru/eng/dm1347
https://doi.org/10.4213/dm1347
https://www.mathnet.ru/eng/dm/v27/i4/p49
This publication is cited in the following 7 articles:
A. S. Tissin, S. A. Kuzmin, “Otsenka krivizny funktsii vydeleniya razryada v dvoichnom predstavlenii chisla”, Diskret. matem., 37:1 (2025), 112–118
D. A. Burov, “On a relationship between linear and differential characteristics of binary vector spaces mappings and diffusion characteristics over blocks of imprimitivity systems of translation group of the binary vector space”, Discrete Math. Appl., 34:3 (2024), 121–144
R. A. de la Cruz Jiménez, “On some properties of the curvature and nondegeneracy of Boolean functions”, Matem. vopr. kriptogr., 13:2 (2022), 65–98
A. S. Tissin, “Curvature of the Boolean majority function”, Discrete Math. Appl., 32:5 (2022), 359–367
S. N. Fedorov, “On a new classification of Boolean functions”, Matem. vopr. kriptogr., 10:2 (2019), 159–168
O. A. Logachev, S. N. Fedorov, V. V. Yashchenko, “On the $\Delta$-equivalence of Boolean functions”, Discrete Math. Appl., 30:2 (2020), 93–101
O. V. Kamlovskii, “Summy modulei koeffitsientov Uolsha–Adamara nekotorykh sbalansirovannykh bulevykh funktsii”, Matem. vopr. kriptogr., 8:4 (2017), 75–98
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