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Mat. Vopr. Kriptogr., 2016, Volume 7, Issue 2, Pages 103–110 (Mi mvk187)  

A graph of minimal distances between bent functions

N. A. Kolomeec

Sobolev Institute of Mathematics SB RAS, Novosibirsk

Abstract: A graph of minimal distances between bent functions is introduced as an undirected graph $(V, E)$, where $V$ is the set of all bent functions in $2k$ variables and $(f, g) \in E$ if the Hamming distance between $f$ and $g$ is equal to $2^k$ (it is the minimal possible distance between two bent functions). It is shown that its subgraph induced by all functions affine equivalent to the Maiorana—McFarland bent functions is connected.

Key words: Boolean functions, bent functions, the minimal distance.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-07-01328_а
Ministry of Education and Science of the Russian Federation NSh-1939.2014.1
The author was supported by the Russian Foundation for Basic Research (project no. 15-07-01328) and by Grant NSh-1939.2014.1 of President of Russia for Leading Scientific Schools.


DOI: https://doi.org/10.4213/mvk187

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UDC: 519.716.322
Received 02.III.2015
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Citation: N. A. Kolomeec, “A graph of minimal distances between bent functions”, Mat. Vopr. Kriptogr., 7:2 (2016), 103–110

Citation in format AMSBIB
\Bibitem{Kol16}
\by N.~A.~Kolomeec
\paper A graph of minimal distances between bent functions
\jour Mat. Vopr. Kriptogr.
\yr 2016
\vol 7
\issue 2
\pages 103--110
\mathnet{http://mi.mathnet.ru/mvk187}
\crossref{https://doi.org/10.4213/mvk187}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3567360}
\elib{https://elibrary.ru/item.asp?id=26475111}


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