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Refinements of Levenshtein Bounds in q-ary Hamming Spaces
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria; Faculty of Engineering, South-Western University, Blagoevgrad, Bulgaria.
Linköping University, Department of Electrical Engineering, Communication Systems.ORCID iD: 0000-0001-5098-9679
Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria.
2018 (English)In: Problems of Information Transmission, ISSN 0032-9460, E-ISSN 1608-3253, Vol. 54, no 4, p. 329-342Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Pleiades Publishing , 2018. Vol. 54, no 4, p. 329-342
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-154151DOI: 10.1134/S0032946018040026ISI: 000456991400002OAI: oai:DiVA.org:liu-154151DiVA, id: diva2:1283681
Available from: 2019-01-29 Created: 2019-01-29 Last updated: 2019-10-09

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Publisher's full texthttps://doi.org/10.1134/S0032946018040026

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Danev, Danyo

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