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On distance Gray codes. / Bykov, I. S.; Perezhogin, A. L.

In: Journal of Applied and Industrial Mathematics, Vol. 11, No. 2, 01.04.2017, p. 185-192.

Research output: Contribution to journal › Article › peer-review

Harvard

Bykov, IS & Perezhogin, AL 2017, 'On distance Gray codes', Journal of Applied and Industrial Mathematics, vol. 11, no. 2, pp. 185-192. https://doi.org/10.1134/S1990478917020041

APA

Bykov, I. S., & Perezhogin, A. L. (2017). On distance Gray codes. Journal of Applied and Industrial Mathematics, 11(2), 185-192. https://doi.org/10.1134/S1990478917020041

Vancouver

Bykov IS, Perezhogin AL. On distance Gray codes. Journal of Applied and Industrial Mathematics. 2017 Apr 1;11(2):185-192. doi: 10.1134/S1990478917020041

Author

Bykov, I. S. ; Perezhogin, A. L. / On distance Gray codes. In: Journal of Applied and Industrial Mathematics. 2017 ; Vol. 11, No. 2. pp. 185-192.

BibTeX

@article{1478cd7edc9148389cd0a4fcba22edf6,
title = "On distance Gray codes",
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.",
keywords = "antipodal Gray code, Gray code, Hamiltonian cycle, n-cube, uniform Gray code",
author = "Bykov, {I. S.} and Perezhogin, {A. L.}",
year = "2017",
month = apr,
day = "1",
doi = "10.1134/S1990478917020041",
language = "English",
volume = "11",
pages = "185--192",
journal = "Journal of Applied and Industrial Mathematics",
issn = "1990-4789",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "2",

}

RIS

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 -

ID: 10040038