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Diskretn. Anal. Issled. Oper., 2012, Volume 19, Number 1, Pages 3–16 (Mi da673)  

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

On reconstructive sets of vertices in the Boolean cube

A. Yu. Vasil'eva

S. L. Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia

Abstract: The notion of a reconstructive set of the Boolean cube is introduced in terms of Fourier transform. The characterization of linear reconstructive sets is obtained. Necessary and sufficient conditions of the reconstructivity of a sphere are established. Sufficient conditions of the reconstructivity of two concentric spheres are found. Bibliogr. 9.

Keywords: Fourier transform, reconstructive set, linear subspace, Krawtchouk polynomial, Johnson scheme.

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English version:
Journal of Applied and Industrial Mathematics, 2012, 6:3, 393–402

Bibliographic databases:

UDC: 519.8
Received: 25.05.2011
Revised: 09.09.2011

Citation: A. Yu. Vasil'eva, “On reconstructive sets of vertices in the Boolean cube”, Diskretn. Anal. Issled. Oper., 19:1 (2012), 3–16; J. Appl. Industr. Math., 6:3 (2012), 393–402

Citation in format AMSBIB
\Bibitem{Vas12}
\by A.~Yu.~Vasil'eva
\paper On reconstructive sets of vertices in the Boolean cube
\jour Diskretn. Anal. Issled. Oper.
\yr 2012
\vol 19
\issue 1
\pages 3--16
\mathnet{http://mi.mathnet.ru/da673}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2961448}
\transl
\jour J. Appl. Industr. Math.
\yr 2012
\vol 6
\issue 3
\pages 393--402
\crossref{https://doi.org/10.1134/S1990478912030155}


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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. A. Yu. Vasil'eva, “Local distributions and reconstruction of hypercube eigenfunctions”, Problems Inform. Transmission, 49:1 (2013), 32–39  mathnet  crossref  isi
    2. K. V. Vorobev, “On the embedding of eigenfunctions of the Johnson graph into eigenfunctions of the Hamming graph”, J. Appl. Industr. Math., 8:1 (2014), 136–142  mathnet  crossref  mathscinet
    3. A. Yu. Vasil'eva, “Reconstruction of eigenfunctions of a $q$-ary $n$-dimensional hypercube”, Problems Inform. Transmission, 51:3 (2015), 231–239  mathnet  crossref  isi  elib
  • Дискретный анализ и исследование операций
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