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New binary h-generator quasi-cyclic codes by augmentation and new minimum distance bounds
Kristianstad University, School of Health and Society, Avdelningen för Design och datavetenskap.ORCID iD: 0000-0002-2492-7754
2016 (English)In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 80, no 1, 1-10 p.Article in journal (Refereed) Published
Abstract [en]

An [n, k, d] code is a binary linear code of block length n, dimension k and minimum Hamming distance d. Since the minimum distance determines the error detection or correction capability, it is desired that d is as large as possible for the given block length n and dimension k. One of the most fundamental problems in coding theory is to construct codes with best possible minimum distances. This problem is very difficult in both theory and practice. During the last decades, it has proved that the class of quasi-cyclic (QC) codes contain many such codes. In this paper, augmentation of binary QC codes is studied. A new augmentation algorithm is presented, and 10 new h-generator QC codes that are better than previously known code have been constructed. Furthermore, Construction X has been applied to obtain another 18 new improved binary linear codes.With the standard construction techniques, a total of 124 new binary linear codes that improve the lower bound on the minimum distance have been obtained.

Place, publisher, year, edition, pages
2016. Vol. 80, no 1, 1-10 p.
Keyword [en]
Best-known codes, Coding theory, Search algorithm, Linear codes, Quasi-cyclic codes, Construction X
National Category
Computer Science
Identifiers
URN: urn:nbn:se:hkr:diva-13742DOI: 10.1007/s10623-015-0059-5ISI: 000377188000001OAI: oai:DiVA.org:hkr-13742DiVA: diva2:797643
Available from: 2015-03-24 Created: 2015-03-24 Last updated: 2017-02-28Bibliographically approved

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Chen, Eric Zhi
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Avdelningen för Design och datavetenskap
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CiteExportLink to record
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Citation style
  • apa
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  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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  • text
  • asciidoc
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