This article is cited in 4 papers

Coding Theory

On metric dimension of nonbinary Hamming spaces

G. A. Kabatiansky^a, V. S. Lebedev<sup>b

a</sup> 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.

UDC: 621.391.15

Received: 10.12.2017
Revised: 25.12.2017

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

Bibliographic databases:

• 
• 
•