Email this article On distance Gray codes
- Authors: Bykov I.S.1, Perezhogin A.L.1,2
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Affiliations:
- Novosibirsk State University
- Sobolev Institute of Mathematics
- Issue: Vol 11, No 2 (2017)
- Pages: 185-192
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/212673
- DOI: https://doi.org/10.1134/S1990478917020041
- ID: 212673
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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.
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About the authors
I. S. Bykov
Novosibirsk State University
Author for correspondence.
Email: patrick.no10@gmail.com
Russian Federation, ul. Pirogova 2, Novosibirsk, 630090
A. L. Perezhogin
Novosibirsk State University; Sobolev Institute of Mathematics
Email: patrick.no10@gmail.com
Russian Federation, ul. Pirogova 2, Novosibirsk, 630090; pr. Akad. Koptyuga 4, Novosibirsk, 630090
