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

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Prikladnaya Diskretnaya Matematika, 2014, Number 3(25), Pages 28–39 (Mi pdm466)

This article is cited in 14 scientific papers (total in 14 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

Full-text PDF (591 kB) Citations (14)

References:

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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.

Document Type: Article

UDC: 519.7

Language: Russian

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}

Linking options:

https://www.mathnet.ru/eng/pdm466

https://www.mathnet.ru/eng/pdm/y2014/i3/p28

Cycle of papers

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
Prikl. Diskr. Mat. Suppl., 2014:7, 22–24
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
Prikl. Diskr. Mat., 2014:3(25), 28–39

This publication is cited in the following 14 articles:

D. A. Bykov, N. A. Kolomeets, “O chisle blizhaishikh bent-funktsii k nekotorym bent-funktsiyam Meiorana — MakFarlanda”, PDM. Prilozhenie, 2024, no. 17, 24–27
D. A. Bykov, “O dostizhimosti nizhnei otsenki chisla bent-funktsii na minimalnom rasstoyanii ot bent-funktsii iz klassa Meiorana — MakFarlanda”, PDM. Prilozhenie, 2023, no. 16, 14–18
D. A. Bykov, N. A. Kolomeets, “O nizhnei otsenke chisla bent-funktsii na minimalnom rasstoyanii ot bent-funktsii iz klassa Meiorana–Makfarlanda”, Diskretn. analiz i issled. oper., 30:3 (2023), 57–80
A. A. Babueva, O. A. Logachev, V. V. Yashchenko, “On the relationship between local affinities of a Boolean function and some types of its degeneracy”, Discrete Math. Appl., 33:6 (2023), 339–353
D. A. Bykov, “O nizhnei otsenke chisla bent-funktsii na minimalnom rasstoyanii ot bent-funktsii iz klassa Meiorana — MakFarlanda”, PDM. Prilozhenie, 2022, no. 15, 22–25
A. K. Oblaukhov, “On metric complements and metric regularity in finite metric spaces”, PDM, 2020, no. 49, 35–45
A. S. Shaporenko, “Svyaz odnorodnykh bent-funktsii i grafov Negi”, Diskretn. analiz i issled. oper., 26:4 (2019), 121–131
N. A. Kolomeets, “Konstruktsiya bent-funktsii po bent-funktsii, affinnoi na neskolkikh sdvigakh podprostranstva”, PDM. Prilozhenie, 2017, no. 10, 41–42
N. Kolomeec, “The graph of minimal distances of bent functions and its properties”, Designs Codes Cryptogr., 85:3 (2017), 395–410
N. A. Kolomeec, “A graph of minimal distances between bent functions”, Matem. vopr. kriptogr., 7:2 (2016), 103–110
N. A. Kolomeets, “O rasstoyanii Khemminga mezhdu dvumya bent-funktsiyami”, PDM. Prilozhenie, 2016, no. 9, 27–28
N. A. Kolomeets, “O svyaznosti grafa minimalnykh rasstoyanii mnozhestva bent-funktsii”, PDM. Prilozhenie, 2015, no. 8, 33–34
V. N. Potapov, “Svoistva $p$ -ichnykh bent-funktsii, nakhodyaschikhsya na minimalnom rasstoyanii drug ot druga”, PDM. Prilozhenie, 2015, no. 8, 39–43
N. N. Tokareva, “O razlozhenii dualnoi bent-funktsii v summu dvukh bent-funktsii”, PDM, 2014, no. 4(26), 59–61

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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