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Prikl. Diskr. Mat., 2013, Number 1(19), Pages 17–33 (Mi pdm400)  

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

Theoretical Foundations of Applied Discrete Mathematics

Binary representations of underdetermined data and superimposed codes

L. A. Sholomov

Institute of Systems Analysis, Russian Academy of Sciences

Abstract: For underdetermined data, binary representations are defined, making it possible to reconstruct the initial data entirely (not only their specifications) and being fairly compact. To solve the problem of their design, some special matrices called selective ones are introduced and studied. They generalize the disjunct (cover-free) matrices widely applied in Computer Science. Some characteristics of selective matrices and estimates of data representation length via some data parameters are investigated. Problems related to the complexity of representations design are considered too.

Keywords: underdetermined data, compression, binary representation, sets system basis, representation length, disjunct matrix, superimposed code, cover-free family, polynomial algorithm.

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UDC: 621.391: 519.728

Citation: L. A. Sholomov, “Binary representations of underdetermined data and superimposed codes”, Prikl. Diskr. Mat., 2013, no. 1(19), 17–33

Citation in format AMSBIB
\Bibitem{Sho13}
\by L.~A.~Sholomov
\paper Binary representations of underdetermined data and superimposed codes
\jour Prikl. Diskr. Mat.
\yr 2013
\issue 1(19)
\pages 17--33
\mathnet{http://mi.mathnet.ru/pdm400}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. A. Sholomov, “Ekonomnoe predstavlenie nedoopredelennykh dannykh i diz'yunktivnye kody”, PDM. Prilozhenie, 2013, no. 6, 27–29  mathnet
    2. V. Yu. Shchukin, “List decoding for a multiple access hyperchannel”, Problems Inform. Transmission, 52:4 (2016), 329–343  mathnet  crossref  isi  elib
    3. A. G. D'yachkov, I. V. Vorobyev, N. A. Polyanskii, V. Yu. Shchukin, “Symmetric disjunctive list-decoding codes”, Designs Codes Cryptogr., 82:1-2, SI (2017), 211–229  crossref  mathscinet  zmath  isi  scopus
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