Volume 24, No 2, 2017, P. 5-17
I. S. Bykov and A. L. Perezhogin
On distance Gray codes
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.
Igor S. Bykov 2
Alexey L. Perezhogin 1,2
1. Sobolev Institute of Mathematics,
4 Koptyug Ave., 630090 Novosibirsk, Russia
2. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia
e-mail: firstname.lastname@example.org, email@example.com
Received 19 May 2016
Revised 16 September 2016
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