Antipodal Gray codes
type: Item
instance of: scholarly article
title: Antipodal Gray codes
zbMATH Open document ID: 1054.94020
author: Charles E. Killian
author: Carla D. Savage
published in: Discrete Mathematics
publication date: 2004-08-06T00:00:00Z
review text: In a private e-mail communication, Snevily (2000) found \(n\)-bit antipodal Gray codes for \(n= 1,2,3,4\) and posed a problem whether they exist for larger \(n\). This paper gives a partial answer to this question. It is proved that for odd \(n> 3\), an \(n\)-bit antipodal Gray code is not possible. The authors made an exhaustive computer search showing that there exists no 6-bit antipodal Gray code. However, it is shown that when \(n\) is power of 2, \(n\)-bit antipodal Gray codes do exist, and the authors provide a recursive construction. The paper concludes with some remaining open cases.
reviewed by: Bai Kishan Dass
Mathematics Subject Classification ID: 94B60
Mathematics Subject Classification ID: 94B25
zbMATH DE Number: 2083671
zbMATH Keywords: antipodal Gray code
zbMATH Keywords: \(n\)-cube
zbMATH Keywords: Hamiltonian cycle
MaRDI profile type: Publication
full work available at URL: j.disc.2003.07.012
OpenAlex ID: W2153332879
cites work: Transition restricted Gray codes
cites work: Q3816026
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cites work: Counting sequences
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DOI: 10.1016/J.DISC.2003.07.012
description: scientific article; zbMATH DE number 2083671