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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

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Spelling suggestions: "subject:"gröbnerbas"" "subject:"gröbnerbasis""

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A Gröbner basis algorithm for fast encoding of Reed-Müller codes

Abrahamsson, Olle January 2016 (has links)
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.
Gröbner basis
error correcting codes
coding theory
algebra
Reed-Müller
Gröbnerbas
felrättande koder
kodningsteori
algebra
Reed-Müller
Algebra and Logic
Algebra och logik

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