Sökning: "Gröbnerbas"

Hittade 1 uppsats innehållade ordet Gröbnerbas.

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

    Kandidat-uppsats, Linköpings universitet/Matematik och tillämpad matematik; Linköpings universitet/Tekniska fakulteten

    Författare :Olle Abrahamsson; [2016]
    Nyckelord :Gröbner basis; error correcting codes; coding theory; algebra; Reed-Müller; Gröbnerbas; felrättande koder; kodningsteori; algebra; Reed-Müller;

    Sammanfattning : 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. LÄS MER