Abstract:
In the paper, we give a review of metrical properties of the entire set of bent functions and its significant subclasses of self-dual and anti-self-dual bent functions. We present results for iterative construction of bent functions in n+2 variables based on the concatenation of four bent functions and consider related open problem proposed by one of the authors. Criterion of self-duality of such functions is discussed. It is explored that the pair of sets of bent functions and affine functions as well as a pair of sets of self-dual and anti-self-dual bent functions in n⩾4 variables is a pair of mutually maximally distant sets that implies metrical duality. Groups of automorphisms of the sets of bent functions and (anti-)self-dual bent functions are discussed. The solution to the problem of preserving bentness and the Hamming distance between bent function and its dual within automorphisms of the set of all Boolean functions in n variables is considered.
Keywords:
Boolean bent function, self-dual bent function, Hamming distance, metrical regularity, automorphism group, iterative construction.
The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation and Laboratory of Cryptography JetBrains Research.
Bibliographic databases:
Document Type:
Article
UDC:519.7
Language: English
Citation:
A. V. Kutsenko, N. N. Tokareva, “Metrical properties of the set of bent functions in view of duality”, Prikl. Diskr. Mat., 2020, no. 49, 18–34
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\by A.~V.~Kutsenko, N.~N.~Tokareva
\paper Metrical properties of the set of bent functions in view of duality
\jour Prikl. Diskr. Mat.
\yr 2020
\issue 49
\pages 18--34
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\crossref{https://doi.org/10.17223/20710410/49/2}
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Linking options:
https://www.mathnet.ru/eng/pdm711
https://www.mathnet.ru/eng/pdm/y2020/i3/p18
This publication is cited in the following 2 articles:
Aleksandr Kutsenko, “Decomposing self-dual bent functions”, Des. Codes Cryptogr., 92:1 (2024), 113
A. V. Kutsenko, “Matritsy Grama bent-funktsii i svoistva podfunktsii kvadratichnykh samodualnykh bent-funktsii”, PDM. Prilozhenie, 2023, no. 16, 26–29