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Diskretnaya Matematika, 2021, Volume 33, Issue 3, Pages 79–91
DOI: https://doi.org/10.4213/dm1635
(Mi dm1635)
 

This article is cited in 5 scientific papers (total in 5 papers)

Criteria for maximal nonlinearity of a function over a finite field

V. G. Ryabov

NPO «GST»
Full-text PDF (532 kB) Citations (5)
References:
Abstract: An $n$-place function over a field with $q$ elements is called maximally nonlinear if it has the greatest nonlinearity among all such functions. Criteria and necessary conditions for maximal nonlinearity are obtained, which imply that, for even $n$, the maximally nonlinear functions are bent functions, but, for $q>2$, the known families of bent functions are not maximally nonlinear. For an arbitrary finite field, a relationship between the Hamming distances from a function to all affine mappings and the Fourier spectra of the nontrivial characters of the function are found.
Keywords: finite field, nonlinearity, affine function, bent function, Fourier coefficients.
Received: 19.01.2021
English version:
Discrete Mathematics and Applications, 2023, Volume 33, Issue 2, Pages 117–126
DOI: https://doi.org/10.1515/dma-2023-0012
Document Type: Article
UDC: 519.716.325+519.719.2
Language: Russian
Citation: V. G. Ryabov, “Criteria for maximal nonlinearity of a function over a finite field”, Diskr. Mat., 33:3 (2021), 79–91; Discrete Math. Appl., 33:2 (2023), 117–126
Citation in format AMSBIB
\Bibitem{Rya21}
\by V.~G.~Ryabov
\paper Criteria for maximal nonlinearity of a function over a finite field
\jour Diskr. Mat.
\yr 2021
\vol 33
\issue 3
\pages 79--91
\mathnet{http://mi.mathnet.ru/dm1635}
\crossref{https://doi.org/10.4213/dm1635}
\transl
\jour Discrete Math. Appl.
\yr 2023
\vol 33
\issue 2
\pages 117--126
\crossref{https://doi.org/10.1515/dma-2023-0012}
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  • https://www.mathnet.ru/eng/dm1635
  • https://doi.org/10.4213/dm1635
  • https://www.mathnet.ru/eng/dm/v33/i3/p79
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Дискретная математика
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    Full-text PDF :69
    References:39
    First page:23
     
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