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Diskretnyi Analiz i Issledovanie Operatsii, 2017, Volume 24, Issue 2, Pages 5–17
DOI: https://doi.org/10.17377/daio.2017.24.545 (Mi da866) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On distance Gray codes

I. S. Bykova, A. L. Perezhoginab

a Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia
b Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
Full-text PDF (295 kB) Citations (2)
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DOI: https://doi.org/10.17377/daio.2017.24.545
Abstract: A Gray code of size $n$ is a cyclic sequence of all binary words of length $n$ such that two consecutive words differ exactly in one position. We say that the Gray code is a distance code if the Hamming distance between words located at distance $k$ from each other is equal to $d$. The distance property generalizes the familiar concepts of a locally balanced Gray code. We prove that there are no distance Gray codes with $d=1$ for $k>1$. Some examples of constructing distance Gray codes are given. For one infinite series of parameters, it is proved that there are no distance Gray codes. Tab. 5, bibliogr. 9.
Keywords: $n$-cube, Hamiltonian cycle, Gray code, uniform Gray code, antipodal Gray code.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00507
Received: 19.05.2016
Revised: 16.09.2016
English version:
Journal of Applied and Industrial Mathematics, 2017, Volume 11, Issue 2, Pages 185–192
DOI: https://doi.org/10.1134/S1990478917020041
Bibliographic databases:
Document Type: Article
UDC: 519.17
Language: Russian
Citation: I. S. Bykov, A. L. Perezhogin, “On distance Gray codes”, Diskretn. Anal. Issled. Oper., 24:2 (2017), 5–17; J. Appl. Industr. Math., 11:2 (2017), 185–192
Citation in format AMSBIB
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\by I.~S.~Bykov, A.~L.~Perezhogin
\paper On distance Gray codes
\jour Diskretn. Anal. Issled. Oper.
\yr 2017
\vol 24
\issue 2
\pages 5--17
\mathnet{http://mi.mathnet.ru/da866}
\crossref{https://doi.org/10.17377/daio.2017.24.545}
\elib{https://elibrary.ru/item.asp?id=29275511}
\transl
\jour J. Appl. Industr. Math.
\yr 2017
\vol 11
\issue 2
\pages 185--192
\crossref{https://doi.org/10.1134/S1990478917020041}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019664778}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Дискретный анализ и исследование операций
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