Email this article On Metric Dimension of Nonbinary Hamming Spaces
- Authors: Kabatiansky G.A.1, Lebedev V.S.2
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Affiliations:
- Skolkovo Institute of Science and Technology
- Kharkevich Institute for Information Transmission Problems
- Issue: Vol 54, No 1 (2018)
- Pages: 48-55
- Section: Coding Theory
- URL: https://journal-vniispk.ru/0032-9460/article/view/166481
- DOI: https://doi.org/10.1134/S0032946018010040
- ID: 166481
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Abstract
For q-ary Hamming spaces we address the problem of the minimum number of points such that any point of the space is uniquely determined by its (Hamming) distances to them. It is conjectured that for a fixed q and growing dimension n of the Hamming space this number asymptotically behaves as 2n/ logqn. We prove this conjecture for q = 3 and q = 4; for q = 2 its validity has been known for half a century.
About the authors
G. A. Kabatiansky
Skolkovo Institute of Science and Technology
Author for correspondence.
Email: g.kabatyansky@skoltech.ru
Russian Federation, Moscow
V. S. Lebedev
Kharkevich Institute for Information Transmission Problems
Email: g.kabatyansky@skoltech.ru
Russian Federation, Moscow
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