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Problemy Peredachi Informatsii, 2010, Volume 46, Issue 3, Pages 60–79 (Mi ppi2022)  

This article is cited in 13 scientific papers (total in 13 papers)

Coding Theory

Eigenspaces of the discrete Walsh transform

M. S. Bespalov

Vladimir State University
References:
Abstract: We refine the notion of a discrete Walsh function and generalize the notion of a discrete Walsh transform, for which we propose a method for generating a corresponding $W$-matrix. We propose spectral decompositions of the discrete Walsh transform operators in arbitrary enumerations, as well as methods for finding bases of eigenspaces, one of them using a new direct product of matrices. We propose a notation for the fast discrete Walsh transform algorithm in the Paley enumeration. We construct Parseval frames for eigenspaces of the discrete Walsh transform in the Paley enumeration and demonstrate methods for applying them in error detection and correction.
Received: 04.02.2010
Revised: 04.05.2010
English version:
Problems of Information Transmission, 2010, Volume 46, Issue 3, Pages 253–271
DOI: https://doi.org/10.1134/S0032946010030051
Bibliographic databases:
Document Type: Article
UDC: 621.391.1+517.984.5
Language: Russian
Citation: M. S. Bespalov, “Eigenspaces of the discrete Walsh transform”, Probl. Peredachi Inf., 46:3 (2010), 60–79; Problems Inform. Transmission, 46:3 (2010), 253–271
Citation in format AMSBIB
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\paper Eigenspaces of the discrete Walsh transform
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\vol 46
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\pages 60--79
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\jour Problems Inform. Transmission
\yr 2010
\vol 46
\issue 3
\pages 253--271
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77958081958}
Linking options:
  • https://www.mathnet.ru/eng/ppi2022
  • https://www.mathnet.ru/eng/ppi/v46/i3/p60
  • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Проблемы передачи информации Problems of Information Transmission
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    Abstract page:908
    Full-text PDF :238
    References:79
    First page:27
     
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