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Probl. Peredachi Inf., 2018, Volume 54, Issue 1, Pages 54–62 (Mi ppi2259)  

Coding Theory

On metric dimension of nonbinary Hamming spaces

G. A. Kabatianskya, V. S. Lebedevb

a Skolkovo Institute of Science and Technology, Moscow, Russia
b Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

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 $2n/\log_qn$. We prove this conjecture for $q=3$ and $q=4$; for $q=2$ its validity has been known for half a century.

Funding Agency Grant Number
Russian Science Foundation 14-50-00150
The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.


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English version:
Problems of Information Transmission, 2018, 54:1, 48–55

Bibliographic databases:

UDC: 621.391.15
Received: 10.12.2017
Revised: 25.12.2017

Citation: G. A. Kabatiansky, V. S. Lebedev, “On metric dimension of nonbinary Hamming spaces”, Probl. Peredachi Inf., 54:1 (2018), 54–62; Problems Inform. Transmission, 54:1 (2018), 48–55

Citation in format AMSBIB
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\paper On metric dimension of nonbinary Hamming spaces
\jour Probl. Peredachi Inf.
\yr 2018
\vol 54
\issue 1
\pages 54--62
\mathnet{http://mi.mathnet.ru/ppi2259}
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\transl
\jour Problems Inform. Transmission
\yr 2018
\vol 54
\issue 1
\pages 48--55
\crossref{https://doi.org/10.1134/S0032946018010040}
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