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Avkodning av cykliska koder - baserad på Euklides algoritm
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
2017 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Decoding of cyclic codes - based on Euclidean algorithm (English)
##### Abstract [en]

Today’s society requires that transformation of information is done effectively and correctly. In other words, the received message must correspond to the message being sent. There are a lot of decoding methods to locate and correct errors. The main purpose in this degree project is to study one of these methods based on the Euclidean algorithm. Thereafter an example will be illustrated showing how the method is used when decoding a three - error correcting BCH code. To begin with, fundamental concepts about coding theory are introduced. Secondly, linear codes, cyclic codes and BCH codes - in that specific order - are explained before advancing to the decoding process. The results show that correcting one or two errors is relatively simple, but when three or more errors occur it becomes much more complicated. In that case, a specific method is required.

##### Abstract [sv]

Dagens samhälle kräver att informationsöverföring sker på ett effektivt och korrekt sätt, det vill säga att den information som når mottagaren motsvarar den som skickades från början. Det finns många avkodningsmetoder för att lokalisera och rätta fel. Syftet i denna uppsats är att studera en av dessa, en som baseras på Euklides algoritm och därefter illustrera ett exempel på hur metoden används vid avkodning av en tre - rättande BCH - kod. Först ges en presentation av grunderna inom kodningsteorin. Sedan introduceras linjära koder, cykliska koder och BCH - koder i nämnd ordning, för att till sist presentera avkodningsprocessen. Det visar sig att det är relativt enkelt att rätta ett eller två fel, men när tre eller fler fel uppstår blir det betydligt mer komplicerat. Då krävs någon speciell metod.

2017. , p. 33
##### Keywords [en]
code word, parity check matrix, generator matrix, syndrome, BCH - code, field extension, Euclidean algorithm method, error locating polynomial
##### Keywords [sv]
kodord, paritetskontrollmatris, generatormatris, syndrom, BCH - kod, kroppsutvidgning, Euklides algoritm - metoden, felsökningspolynom
##### National Category
Natural Sciences Mathematics
##### Identifiers
OAI: oai:DiVA.org:kau-48248DiVA, id: diva2:1086731
Mathematics
##### Educational program
Mathematics Programme (180 ECTS credits)
##### Presentation
2017-01-11, 21E 205 Karlstad universitet, Karlstad Universitetsgatan 2, 651 88, Karlstad, 14:15 (Swedish)
##### Examiners
Available from: 2018-10-17 Created: 2017-04-03 Last updated: 2018-11-20Bibliographically approved

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##### By organisation
Department of Mathematics and Computer Science (from 2013)
##### On the subject
Natural SciencesMathematics

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