RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

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


Diskretn. Anal. Issled. Oper., 2012, Volume 19, Number 1, Pages 41–58 (Mi da676)  

This article is cited in 6 scientific papers (total in 6 papers)

Enumeration of bent functions on the minimal distance from the quadratic bent function

N. A. Kolomeec

S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia

Abstract: Constructing bent functions on the minimal distance from the quadratic bent function is studied. All such bent functions in $2k$ variables are obtained and it is shown that the number of them is equal to $2^k(2^1+1)…(2^k+1)$. A lower bound of the number of bent functions on the minimal distance from a Maiorana–McFarland bent function is given. Tab. 1, bibliogr. 9.

Keywords: bent function, the minimal distance, quadratic bent function.

Full text: PDF file (299 kB)
References: PDF file   HTML file

English version:
Journal of Applied and Industrial Mathematics, 2012, 6:3, 306–317

Bibliographic databases:

UDC: 519.7
Received: 05.04.2011
Revised: 24.09.2011

Citation: N. A. Kolomeec, “Enumeration of bent functions on the minimal distance from the quadratic bent function”, Diskretn. Anal. Issled. Oper., 19:1 (2012), 41–58; J. Appl. Industr. Math., 6:3 (2012), 306–317

Citation in format AMSBIB
\Bibitem{Kol12}
\by N.~A.~Kolomeec
\paper Enumeration of bent functions on the minimal distance from the quadratic bent function
\jour Diskretn. Anal. Issled. Oper.
\yr 2012
\vol 19
\issue 1
\pages 41--58
\mathnet{http://mi.mathnet.ru/da676}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2961451}
\transl
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 3
\pages 306--317
\crossref{https://doi.org/10.1134/S1990478912030052}


Linking options:
  • http://mi.mathnet.ru/eng/da676
  • http://mi.mathnet.ru/eng/da/v19/i1/p41

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. G. I. Shushuev, “Vektornye bulevy funktsii na rasstoyanii odin ot APN-funktsii”, PDM. Prilozhenie, 2014, no. 7, 36–37  mathnet
    2. N. A. Kolomeets, “Verkhnyaya otsenka chisla bent-funktsii na rasstoyanii $2^k$ ot proizvolnoi bent-funktsii ot $2k$ peremennykh”, PDM, 2014, no. 3(25), 28–39  mathnet
    3. V. N. Potapov, “Svoistva $p$-ichnykh bent-funktsii, nakhodyaschikhsya na minimalnom rasstoyanii drug ot druga”, PDM. Prilozhenie, 2015, no. 8, 39–43  mathnet  crossref
    4. N. Kolomeec, “The graph of minimal distances of bent functions and its properties”, Des. Codes Cryptogr., 85:3 (2017), 395–410  crossref  mathscinet  zmath  isi  scopus
    5. Y. Zhao, N. Cao, Zh. Qi, G. Li, P. Liu, “A new algorithm for enumerating bent functions based on truth tables and run length”, IEEE Access, 6 (2018), 23800–23805  crossref  isi  scopus
    6. Zhao Y., Zhang F., Qi Ch., “A Novel Algorithm Enumerating Bent Functions Based on Value Distribution and Run Length”, Lecture Notes in Real-Time Intelligent Systems (Rtis 2016), Advances in Intelligent Systems and Computing, 613, eds. MizeraPietraszko J., Pichappan P., Springer International Publishing Ag, 2018, 250–259  crossref  mathscinet  isi  scopus
  • Дискретный анализ и исследование операций
    Number of views:
    This page:299
    Full text:81
    References:23
    First page:15

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020