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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2022, Volume 19, Issue 1, Pages 342–347
DOI: https://doi.org/10.33048/semi.2022.19.029
(Mi semr1505)
 

Discrete mathematics and mathematical cybernetics

A quadratic part of a bent function can be any

N. N. Tokarevaab

a Sobolev Institute of Mathematics, 4, Koptyuga, ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 2, Pyrogova str., Novosibirsk, 630090, Russia
References:
Abstract: Boolean functions in $n$ variables that are on the maximal possible Hamming distance from all affine Boolean functions in $n$ variables are called bent functions ($n$ is even). They are intensively studied since sixties of XX century in relation to applications in cryptography and discrete mathematics. Often, bent functions are represented in their algebraic normal form (ANF). It is well known that the linear part of ANF of a bent function can be arbitrary. In this note we prove that a quadratic part of a bent function can be arbitrary too.
Keywords: Boolean function, bent function, linear function, quadratic function, homogeneous function.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-281
The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.
Received March 13, 2022, published June 29, 2022
Bibliographic databases:
Document Type: Article
UDC: 512.5
MSC: 13A99
Language: English
Citation: N. N. Tokareva, “A quadratic part of a bent function can be any”, Sib. Èlektron. Mat. Izv., 19:1 (2022), 342–347
Citation in format AMSBIB
\Bibitem{Tok22}
\by N.~N.~Tokareva
\paper A quadratic part of a bent function can be any
\jour Sib. \`Elektron. Mat. Izv.
\yr 2022
\vol 19
\issue 1
\pages 342--347
\mathnet{http://mi.mathnet.ru/semr1505}
\crossref{https://doi.org/10.33048/semi.2022.19.029}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4449221}
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