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Problems of Information Transmission

, Volume 54, Issue 1, pp 48–55 | Cite as

On Metric Dimension of Nonbinary Hamming Spaces

  • G. A. Kabatiansky
  • V. S. Lebedev
Coding Theory
  • 35 Downloads

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

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Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Skolkovo Institute of Science and TechnologyMoscowRussia
  2. 2.Kharkevich Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia

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