Problems of Information Transmission

, Volume 54, Issue 4, pp 329–342 | Cite as

Refinements of Levenshtein Bounds in q-ary Hamming Spaces

  • P. BoyvalenkovEmail author
  • D. Danev
  • M. Stoyanova
Coding Theory


We develop refinements of the Levenshtein bound in q-ary Hamming spaces by taking into account the discrete nature of the distances versus the continuous behavior of certain parameters used by Levenshtein. We investigate the first relevant cases and present new bounds. In particular, we derive generalizations and q-ary analogs of the MacEliece bound. Furthermore, we provide evidence that our approach is as good as the complete linear programming and discuss how faster are our calculations. Finally, we present a table with parameters of codes which, if exist, would attain our bounds.


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© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Faculty of EngineeringSouth-Western UniversityBlagoevgradBulgaria
  3. 3.Department of Electrical Engineering and Department of MathematicsLinköping UniversityLinköpingSweden
  4. 4.Faculty of Mathematics and InformaticsSofia UniversitySofiaBulgaria

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