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Diskretn. Anal. Issled. Oper., 2017, Volume 24, Number 2, Pages 5–17 (Mi da866)  

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

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


DOI: https://doi.org/10.17377/daio.2017.24.545

Full text: PDF file (295 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2017, 11:2, 185–192

UDC: 519.17
Received: 19.05.2016
Revised: 16.09.2016

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{http://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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019664778}


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