Trudy SPIIRAN
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Informatics and Automation:
Year:
Volume:
Issue:
Page:
Find






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


Trudy SPIIRAN, 2017, Issue 54, Pages 224–243
DOI: https://doi.org/10.15622/sp.54.10
(Mi trspy973)
 

This article is cited in 3 scientific papers (total in 3 papers)

Theoretical and Applied Mathematics

Dynamic generators of the quasiortogonal Hadamard matrix family

N. A. Balonina, M. B. Sergeeva, V. S. Suzdalb

a Saint Petersburg State University of Aerospace Instrumentation (SUAI)
b Institute for Scintillation Materials of National Academy of Sciences of Ukraine
Abstract: The problem of constructing non-linear and linear finite-field generators of quasi-orthogonal matrices of the Hadamard family with a small number of distinct values of their elements not exceeding by absolute value 1 and a global or local maximum of determinant is investigated. The properties of such dynamical systems are analyzed; the classification of the matrix families and their ornaments, obtained with their help, is described; the way of proving the existence of real and integer matrices different from the combinatorial approach is shown. The values to which the elements of the matrix are equal are called its levels. The concepts of the Hadamard norm and the determinant of a quasiorthogonal matrix are introduced. Levels, Hadamard norm and determinant play a fundamental role in the definitions of classes of generalized matrices of the Hadamard family. The classes of the Hadamard, Belevich (conference matrices), Seberri (weighing matrices), Mersenne, Euler, Odin (Seidel), Fermat matrices are described. The formulas for the values of their levels are given. Ornaments of Euler matrices answer to the question of the maximum complexity of Hadamard matrices — two border two circulant structure.
Keywords: dynamical systems; quasiorthogonal matrices; deterministic chaos; finite fields.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 2.2200.2017/4.6
The research leading to these results has received funding from the Ministry of Education and Science of the Russian Federation according to the project part of the state funding assignment No 2.2200.2017/4.6.
Bibliographic databases:
Document Type: Article
UDC: 519.61:511-33
Language: Russian
Citation: N. A. Balonin, M. B. Sergeev, V. S. Suzdal, “Dynamic generators of the quasiortogonal Hadamard matrix family”, Tr. SPIIRAN, 54 (2017), 224–243
Citation in format AMSBIB
\Bibitem{BalSerSuz17}
\by N.~A.~Balonin, M.~B.~Sergeev, V.~S.~Suzdal
\paper Dynamic generators of the quasiortogonal Hadamard matrix family
\jour Tr. SPIIRAN
\yr 2017
\vol 54
\pages 224--243
\mathnet{http://mi.mathnet.ru/trspy973}
\crossref{https://doi.org/10.15622/sp.54.10}
\elib{https://elibrary.ru/item.asp?id=30282027}
Linking options:
  • https://www.mathnet.ru/eng/trspy973
  • https://www.mathnet.ru/eng/trspy/v54/p224
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Informatics and Automation
    Statistics & downloads:
    Abstract page:124
    Full-text PDF :45
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024