Diskretnyi Analiz i Issledovanie Operatsii
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Diskretn. Anal. Issled. Oper.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Diskretnyi Analiz i Issledovanie Operatsii, 2021, Volume 28, Issue 2, Pages 74–91
DOI: https://doi.org/10.33048/daio.2021.28.700 (Mi da1278) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On degree of nonlinearity of the coordinate polynomials for a product of transformations of a binary vector space

V. M. Fomichevabc

a Financial University under the Government of the Russian Federation, 49 Leningradskii Avenue, 125993 Moscow, Russia
b Security Code LLC, 10 Bld. 1 Pervyi Nagatinskii Driveway, 115230 Moscow, Russia
c Institute of Informatics Problems of FRC CSC RAS, 44 Bld. 2 Vavilov Street, 119333 Moscow, Russia
Full-text PDF (347 kB) Citations (4)
References:
PDF
HTML
DOI: https://doi.org/10.33048/daio.2021.28.700
Abstract: We construct a nonnegative integer matrix to evaluate the matrix of nonlinearity characteristics for the coordinate polynomials of a product of transformations of a binary vector space. The matrix of the characteristics of the transformation is defined by the degrees of nonlinearity of the derivatives of all coordinate functions with respect to each input variable. The entries of the evaluation matrix are expressed in terms of the characteristics of the coordinate polynomials of the multiplied transformations. Calculation of the evaluation matrix is easier than calculating the exact values of the characteristics. The estimation method is extended to an arbitrary number of multiplied transformations. Computational examples are given that in particular show the accuracy of the obtained estimates and the domain of their nontriviality. Tab. 1, bibliogr. 18.
Keywords: coordinate polynomial of transformation, maximal monomial of a polynomial, degree of a polynomial.
Received: 28.09.2020
Revised: 15.02.2021
Accepted: 19.02.2021
English version:
Journal of Applied and Industrial Mathematics, 2021, Volume 15, Issue 2, Pages 212–222
DOI: https://doi.org/10.1134/S1990478921020034
Bibliographic databases:
Document Type: Article
UDC: 519.17
Language: Russian
Citation: V. M. Fomichev, “On degree of nonlinearity of the coordinate polynomials for a product of transformations of a binary vector space”, Diskretn. Anal. Issled. Oper., 28:2 (2021), 74–91; J. Appl. Industr. Math., 15:2 (2021), 212–222
Citation in format AMSBIB
\Bibitem{Fom21}
\by V.~M.~Fomichev
\paper On~degree of~nonlinearity of~the~coordinate polynomials for~a~product of transformations of~a~binary vector space
\jour Diskretn. Anal. Issled. Oper.
\yr 2021
\vol 28
\issue 2
\pages 74--91
\mathnet{http://mi.mathnet.ru/da1278}
\crossref{https://doi.org/10.33048/daio.2021.28.700}
\transl
\jour J. Appl. Industr. Math.
\yr 2021
\vol 15
\issue 2
\pages 212--222
\crossref{https://doi.org/10.1134/S1990478921020034}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85116200845}
Linking options:
  • https://www.mathnet.ru/eng/da1278
  • https://www.mathnet.ru/eng/da/v28/i2/p74
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Дискретный анализ и исследование операций
    Statistics & downloads:
    Abstract page:187
    Full-text PDF :46
    References:18
    First page:5
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024