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English version:
Journal of Applied and Industrial Mathematics, 2016, 10:1, 78-85

Volume 23, No 1, 2016, P. 51-64

UDC 519.95
I. S. Bykov
On locally balanced Gray codes

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 ≥ 3 there exists a Gray code with window width not greater than $n + 3 \lfloor\log n\rfloor$.
Tab. 2, bibliogr. 10.

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

DOI: 10.17377/daio.2016.23.497

Igor S. Bykov 1
1. Sobolev Institute of Mathematics,
4 Koptyug Ave., 630090 Novosibirsk, Russia
e-mail: patrick.no10@gmail.com

Received 9 June 2015
Revised 17 August 2015

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 © Sobolev Institute of Mathematics, 2015