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Prikl. Diskr. Mat., 2014, Number 3(25), Pages 28–39 (Mi pdm466)  

This article is cited in 8 scientific papers (total in 8 papers)

Theoretical Foundations of Applied Discrete Mathematics

An upper bound for the number of bent functions at the distance $2^k$ from an arbitrary bent function in $2k$ variables

N. A. Kolomeec

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: An upper bound for the number of bent functions at the distance $2^k$ from an arbitrary bent function in $2k$ variables is obtained. The bound is reached only for quadratic bent functions. A notion of completely affine decomposable Boolean function is introduced. It is proved that only affine and quadratic Boolean functions can be completely affine decomposable.

Keywords: Boolean functions, bent functions, quadratic bent functions.

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UDC: 519.7

Citation: N. A. Kolomeec, “An upper bound for the number of bent functions at the distance $2^k$ from an arbitrary bent function in $2k$ variables”, Prikl. Diskr. Mat., 2014, no. 3(25), 28–39

Citation in format AMSBIB
\Bibitem{Kol14}
\by N.~A.~Kolomeec
\paper An upper bound for the number of bent functions at the distance $2^k$ from an arbitrary bent function in $2k$ variables
\jour Prikl. Diskr. Mat.
\yr 2014
\issue 3(25)
\pages 28--39
\mathnet{http://mi.mathnet.ru/pdm466}


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    This publication is cited in the following articles:
    1. N. N. Tokareva, “O razlozhenii dualnoi bent-funktsii v summu dvukh bent-funktsii”, PDM, 2014, no. 4(26), 59–61  mathnet
    2. N. A. Kolomeets, “O svyaznosti grafa minimalnykh rasstoyanii mnozhestva bent-funktsii”, PDM. Prilozhenie, 2015, no. 8, 33–34  mathnet  crossref
    3. V. N. Potapov, “Svoistva $p$-ichnykh bent-funktsii, nakhodyaschikhsya na minimalnom rasstoyanii drug ot druga”, PDM. Prilozhenie, 2015, no. 8, 39–43  mathnet  crossref
    4. N. A. Kolomeec, “A graph of minimal distances between bent functions”, Matem. vopr. kriptogr., 7:2 (2016), 103–110  mathnet  crossref  mathscinet  elib
    5. N. A. Kolomeets, “O rasstoyanii Khemminga mezhdu dvumya bent-funktsiyami”, PDM. Prilozhenie, 2016, no. 9, 27–28  mathnet  crossref
    6. N. A. Kolomeets, “Konstruktsiya bent-funktsii po bent-funktsii, affinnoi na neskolkikh sdvigakh podprostranstva”, PDM. Prilozhenie, 2017, no. 10, 41–42  mathnet  crossref
    7. N. Kolomeec, “The graph of minimal distances of bent functions and its properties”, Designs Codes Cryptogr., 85:3 (2017), 395–410  crossref  mathscinet  zmath  isi  scopus
    8. A. S. Shaporenko, “Svyaz odnorodnykh bent-funktsii i grafov Negi”, Diskretn. analiz i issled. oper., 26:4 (2019), 121–131  mathnet  crossref
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