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A Gröbner basis algorithm for fast encoding of Reed-Müller codes
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2016 (English)Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
Abstract [en]

In this thesis the relationship between Gröbner bases and algebraic coding theory is investigated, and especially applications towards linear codes, with Reed-Müller codes as an illustrative example. We prove that each linear code can be described as a binomial ideal of a polynomial ring, and that a systematic encoding algorithm for such codes is given by the remainder of the information word computed with respect to the reduced Gröbner basis. Finally we show how to apply the representation of a code by its corresponding polynomial ring ideal to construct a class of codes containing the so called primitive Reed-Müller codes, with a few examples of this result.

Place, publisher, year, edition, pages
2016. , 35 p.
Series
, LiTH-MAT-EX, 2016/06
Keyword [en]
Gröbner basis, error correcting codes, coding theory, algebra, Reed-Müller
Keyword [sv]
Gröbnerbas, felrättande koder, kodningsteori, algebra, Reed-Müller
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:liu:diva-132429ISRN: LiTH-MAT-EX–2016/06–SEOAI: oai:DiVA.org:liu-132429DiVA: diva2:1045846
Subject / course
Mathematics
Supervisors
Examiners
Available from: 2016-11-16 Created: 2016-11-10 Last updated: 2016-11-16Bibliographically approved

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Abrahamsson, Olle
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Mathematics and Applied MathematicsFaculty of Science & Engineering
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