TY - JOUR

T1 - On distance Gray codes

AU - Bykov, I. S.

AU - Perezhogin, A. L.

PY - 2017/4/1

Y1 - 2017/4/1

N2 - 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.

AB - 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.

KW - antipodal Gray code

KW - Gray code

KW - Hamiltonian cycle

KW - n-cube

KW - uniform Gray code

UR - http://www.scopus.com/inward/record.url?scp=85019664778&partnerID=8YFLogxK

U2 - 10.1134/S1990478917020041

DO - 10.1134/S1990478917020041

M3 - Article

AN - SCOPUS:85019664778

VL - 11

SP - 185

EP - 192

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 2

ER -