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Sib. Èlektron. Mat. Izv., 2016, Volume 13, Pages 1346–1368 (Mi semr755)  

Discrete mathematics and mathematical cybernetics

On plateaued Boolean functions with the same spectrum support

A. V. Khalyavina, M. S. Lobanovb, Yu. V. Tarannikovb

a Yandex, 16, Leo Tolstoy St., 119021, Moscow, Russia
b Mech. & Math. Department, Lomonosov Moscow State University, 119992, Moscow, Russia

Abstract: In the first half of the paper we give a brief review of plateaued functions, regular functions and related topics including connections with problems on subgraphs of the Hamming graph. In the second half of the paper we discover wide infinite families of spectrum supports for which it is possible to count the number of plateaued Boolean functions with such spectrum supports and give corresponding formulas; only one infinite sequence of such spectrum supports was known before.

Keywords: plateaued functions, Boolean functions, Walsh Spectrum, Fourier spectrum, spectra, spectrum support, spectral analysis, regular functions, correlation immune functions, $m$-resilient functions, address function, recursive constructions, Hamming graph, regular graphs, equitable partitions, symmetries.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00226_
The work of the third author is supported by RFBR, grant 160100226.


DOI: https://doi.org/10.17377/semi.2016.13.105

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Bibliographic databases:

Document Type: Article
UDC: 519.115.4
MSC: 06E30
Received November 7, 2016, published December 26, 2016
Language: English

Citation: A. V. Khalyavin, M. S. Lobanov, Yu. V. Tarannikov, “On plateaued Boolean functions with the same spectrum support”, Sib. Èlektron. Mat. Izv., 13 (2016), 1346–1368

Citation in format AMSBIB
\Bibitem{KhaLobTar16}
\by A.~V.~Khalyavin, M.~S.~Lobanov, Yu.~V.~Tarannikov
\paper On plateaued Boolean functions with the same spectrum support
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 1346--1368
\mathnet{http://mi.mathnet.ru/semr755}
\crossref{https://doi.org/10.17377/semi.2016.13.105}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000407781100105}


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