M. S. Bespalov, “Eigenspaces of the discrete Walsh transform”, Probl. Peredachi Inf., 46:3 (2010), 60–79; Problems Inform. Transmission, 46:3 (2010), 253

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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

Full-text PDF (333 kB) Citations (13)

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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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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:

Yabin Xing, Yan Hong, Limin Gao, Ting Gao, Fengli Yan, “Efficient detection for quantum states containing fewer than k unentangled particles in multipartite quantum systems”, Quantum Inf Process, 23:1 (2024)
S. Ya. Novikov, V. V. Sevost'yanova, “Maltsev equal-norm tight frames”, Izv. Math., 86:4 (2022), 770–781
M. S. Bespalov, “Politsirkulyantnye matritsy v diskretnom garmonicheskom analize”, Materialy 20 Mezhdunarodnoi Saratovskoi zimnei shkoly «Sovremennye problemy teorii funktsii i ikh prilozheniya», Saratov, 28 yanvarya — 1 fevralya 2020 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 200, VINITI RAN, M., 2021, 11–28
M. S. Bespalov, K. M. Malkova, “Kodirovanie informatsii matritsami Uolsha”, PDM. Prilozhenie, 2020, no. 13, 121–124
M. S. Bespalov, M. S. Bespalov, “Extraction of Walsh Harmonics by Linear Combinations of Dyadic Shifts”, J Math Sci, 249:6 (2020), 838
Yu. A. Farkov, M. G. Robakidze, “Parseval Frames and the Discrete Walsh Transform”, Math. Notes, 106:3 (2019), 446–456
Yu. A. Farkov, “Finite Parseval frames in Walsh analysis”, J. Math. Sci. (N. Y.), 263:4 (2022), 579–589
M. S. Bespalov, “New Good's type Kronecker power expansions”, Problems Inform. Transmission, 54:3 (2018), 253–257
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
M. S. Bespalov, “Generating operator for discrete Chrestenson functions”, Problems Inform. Transmission, 51:1 (2015), 37–48
M. S. Bespalov, “Cyclic Operators for Columns of the Matrices of Discrete Transforms”, J Math Sci, 208:1 (2015), 36
M. S. Bespalov, “On the properties of a new tensor product of matrices”, Comput. Math. Math. Phys., 54:4 (2014), 547–561
M. S. Bespalov, “Discrete Chrestenson transform”, Problems Inform. Transmission, 46:4 (2010), 353–375

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

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Abstract page:	954
Full-text PDF :	255
References:	93
First page:	27

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