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New quasi-twisted codes over F11— minimum distance bounds and a new database
Kristianstad University, School of Health and Society, Avdelningen för Design och datavetenskap. (Computer Science)ORCID iD: 0000-0002-2492-7754
USA.
2015 (English)In: Journal of Information and Optimization Sciences, ISSN 0252-2667, E-ISSN 2169-0103, Vol. 36, no 1-2, 129-157 p.Article in journal (Refereed) Published
Abstract [en]

One fundamental and challenging problem in coding theory is to optimize the parameters [nk,d] of a linear code over the finite field Fq and construct codes with best possible parameters. There are tables and databases of best-known linear codes over the finite fields of size up to 9 together with upper bounds on the minimum distances. Motivated by recent works on codes over F11, we present a table of best-known linear codes over F11 together with upper bounds on minimum distances. Our table covers the range n ≤ 150 for the length, and 3 ≤ k ≤ 7 for the dimension. To the best of our knowledge, this is the first time such a table is presented in the literature. For the construction of the best-known codes, we employed an iterative heuristic search algorithm to search for new linear codes in the class of quasi-twisted (QT) codes. The search yielded many new codes with better parameters than previously known codes. In many cases, optimal codes are obtained. In addition to presenting a comprehensive table of best-known codes over F11 of dimensions up to 7 with upper bounds on the minimum distances, we also present separate tables for the optimal codes and new QT codes over F11. We hope that this work will be a useful source for further study on codes over F11.

Place, publisher, year, edition, pages
2015. Vol. 36, no 1-2, 129-157 p.
Keyword [en]
Quasi-twisted codes, heuristic search algorithm, iterative search, distance bounds
National Category
Computer Science
Identifiers
URN: urn:nbn:se:hkr:diva-13778DOI: 10.1080/02522667.2014.961788OAI: oai:DiVA.org:hkr-13778DiVA: diva2:800862
Available from: 2015-04-08 Created: 2015-04-08 Last updated: 2016-01-07Bibliographically approved

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Chen, Eric Zhi
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Avdelningen för Design och datavetenskap
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf