On distance Gray codes Full article
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Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797 |
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| Output data | Year: 2017, Volume: 11, Number: 2, Pages: 185-192 Pages count : 8 DOI: 10.1134/s1990478917020041 | ||||
| Tags | n-cube, Hamiltonian cycle, Gray code, uniform Gray code, antipodal Gray code | ||||
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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.
Cite:
Bykov I.S.
, Perezhogin A.L.
On distance Gray codes
Journal of Applied and Industrial Mathematics. 2017. V.11. N2. P.185-192. DOI: 10.1134/s1990478917020041 Scopus РИНЦ OpenAlex
On distance Gray codes
Journal of Applied and Industrial Mathematics. 2017. V.11. N2. P.185-192. DOI: 10.1134/s1990478917020041 Scopus РИНЦ OpenAlex
Original:
Быков И.С.
, Пережогин А.Л.
О дистанционных кодах Грея
Дискретный анализ и исследование операций. 2017. Т.24. №2. С.5-17. DOI: 10.17377/daio.2017.24.545 РИНЦ
О дистанционных кодах Грея
Дискретный анализ и исследование операций. 2017. Т.24. №2. С.5-17. DOI: 10.17377/daio.2017.24.545 РИНЦ
Dates:
| Submitted: | May 19, 2016 |
| Published online: | May 25, 2017 |
Identifiers:
| Scopus: | 2-s2.0-85019664778 |
| Elibrary: | 31033167 |
| OpenAlex: | W2619231335 |