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1	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
2	Protichybové zabezpečení v digitálních komunikačních systémech / Forward Error Correction in Digital Communication Systems Kostrhoun, Jan January 2013 (has links) This work deals with forward error correction. In the work, basic methods and algorithms of error correction are described. For the presentation of encoding and decoding process of Hamming code, Reed-Müller code, Fire code, Reed-Solomon code and Trellis coded modulation programs in Matlab were created.