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Probl. Peredachi Inf., 2010, Volume 46, Issue 3, Pages 60–79 (Mi ppi2022)  

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

Coding Theory

Eigenspaces of the discrete Walsh transform

M. S. Bespalov

Vladimir State University

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.

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English version:
Problems of Information Transmission, 2010, 46:3, 253–271

Bibliographic databases:

UDC: 621.391.1+517.984.5
Received: 04.02.2010
Revised: 04.05.2010

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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\by M.~S.~Bespalov
\paper Eigenspaces of the discrete Walsh transform
\jour Probl. Peredachi Inf.
\yr 2010
\vol 46
\issue 3
\pages 60--79
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2766609}
\transl
\jour Problems Inform. Transmission
\yr 2010
\vol 46
\issue 3
\pages 253--271
\crossref{https://doi.org/10.1134/S0032946010030051}
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    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. M. S. Bespalov, “Discrete Chrestenson transform”, Problems Inform. Transmission, 46:4 (2010), 353–375  mathnet  crossref  mathscinet  isi
    2. M. S. Bespalov, “On the properties of a new tensor product of matrices”, Comput. Math. Math. Phys., 54:4 (2014), 547–561  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. M. S. Bespalov, “Generating operator for discrete Chrestenson functions”, Problems Inform. Transmission, 51:1 (2015), 37–48  mathnet  crossref  isi  elib
    4. M. S. Bespalov, A. S. Golubev, A. S. Pochenchuk, “Derivation of fast algorithms via binary filtering of signals”, Problems Inform. Transmission, 52:4 (2016), 359–372  mathnet  crossref  isi  elib
    5. M. S. Bespalov, “New Good's type Kronecker power expansions”, Problems Inform. Transmission, 54:3 (2018), 253–257  mathnet  crossref  isi  elib
    6. Yu. A. Farkov, M. G. Robakidze, “Parseval Frames and the Discrete Walsh Transform”, Math. Notes, 106:3 (2019), 446–456  mathnet  crossref  crossref  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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