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Classification of perfect codes and minimal distances in the Lee metric
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
2010 (English)Independent thesis Advanced level (degree of Master (Two Years)), 15 credits / 22,5 HE creditsStudent thesis
Abstract [en]

Perfect codes and minimal distance of a code have great importance in the study of theoryof codes. The perfect codes are classified generally and in particular for the Lee metric.However, there are very few perfect codes in the Lee metric. The Lee metric hasnice properties because of its definition over the ring of integers residue modulo q. It isconjectured that there are no perfect codes in this metric for q > 3, where q is a primenumber.The minimal distance comes into play when it comes to detection and correction oferror patterns in a code. A few bounds on the number of codewords and minimal distanceof a code are discussed. Some examples for the codes are constructed and their minimaldistance is calculated. The bounds are illustrated with the help of the results obtained.

Place, publisher, year, edition, pages
2010. , p. 63
Keywords [en]
Hamming metric; Lee metric; Perfect codes; Minimal distance
Identifiers
URN: urn:nbn:se:lnu:diva-6574OAI: oai:DiVA.org:lnu-6574DiVA, id: diva2:327206
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2010-06-28 Created: 2010-06-28 Last updated: 2010-06-28Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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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