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Classification of perfect codes and minimal distances in the Lee metric

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.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:lnu-6574
Date January 2010
CreatorsAhmed, Naveed, Ahmed, Waqas
PublisherLinnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM, Linnéuniversitetet, Institutionen för datavetenskap, fysik och matematik, DFM
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, info:eu-repo/semantics/masterThesis, text
Formatapplication/pdf
Rightsinfo:eu-repo/semantics/openAccess

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