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Diskretn. Anal. Issled. Oper., 2016, Volume 23, Number 1, Pages 51–64 (Mi da838)  

This article is cited in 4 scientific papers (total in 4 papers)

On locally balanced Gray codes

I. S. Bykov

Sobolev Institute of Mathematics, 4 Koptyug Ave., 630090 Novosibirsk, Russia

Abstract: We consider locally balanced Gray codes. We say that a Gray code is locally balanced if each “short” subword of transition sequence contains all letters of the set $\{1,2,…,n\}$. The minimal length of such subwords is called the window width of the code. We show that for each $n\ge3$ there exists a Gray code with window width not greater than $n+3\lfloor\log n\rfloor$. Tab. 3, bibliogr. 10.

Keywords: Gray code, Hamilton cycle, $n$-cube, window width code.

DOI: https://doi.org/10.17377/daio.2016.23.497

Full text: PDF file (287 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2016, 10:1, 78–85

Bibliographic databases:

UDC: 519.95
Received: 09.06.2015
Revised: 17.08.2015

Citation: I. S. Bykov, “On locally balanced Gray codes”, Diskretn. Anal. Issled. Oper., 23:1 (2016), 51–64; J. Appl. Industr. Math., 10:1 (2016), 78–85

Citation in format AMSBIB
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\by I.~S.~Bykov
\paper On locally balanced Gray codes
\jour Diskretn. Anal. Issled. Oper.
\yr 2016
\vol 23
\issue 1
\pages 51--64
\mathnet{http://mi.mathnet.ru/da838}
\crossref{https://doi.org/10.17377/daio.2016.23.497}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3555675}
\elib{https://elibrary.ru/item.asp?id=25792212}
\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 1
\pages 78--85
\crossref{https://doi.org/10.1134/S1990478916010099}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84961564563}


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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. I. S. Bykov, A. L. Perezhogin, “On distance Gray codes”, J. Appl. Industr. Math., 11:2 (2017), 185–192  mathnet  crossref  crossref  elib
    2. S. Contassot-Vivier, J.-F. Couchot, Ch. Guyeux, P.-C. Heam, “Random walk in a N-cube without Hamiltonian cycle to chaotic pseudorandom number generation: theoretical and practical considerations”, Int. J. Bifurcation Chaos, 27:1 (2017), 1750014  crossref  mathscinet  zmath  isi  scopus
    3. S. Contassot-Vivier, J.-F. Couchot, P.-C. Heam, “Gray codes generation algorithm and theoretical evaluation of random walks in N-cubes”, Mathematics, 6:6 (2018), 98  crossref  isi  scopus
    4. I. S. Bykov, “$2$-Factors without close edges in the $n$-dimensional cube”, J. Appl. Industr. Math., 13:3 (2019), 405–417  mathnet  crossref  crossref
  • Дискретный анализ и исследование операций
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