RINGS, GROEBNER BASES, AND CODES - Andriatahiny, Harinaivo;Rakotomalala, Vololona Harinoro
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This book contains three parts. Part I provides a new proof of the fact that a finite commutative ring may be expressed as a sum of finite local rings. A Galois ring is constructed within a finite local ring by means of a Teichmuller representation system. Part II presents some variants of the Reed-Muller codes. Part III gives a standard basis for a linear code over a prime field. A decoding algorithm for binary linear codes using a Groebner basis is developed.

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Produktbeschreibung
This book contains three parts. Part I provides a new proof of the fact that a finite commutative ring may be expressed as a sum of finite local rings. A Galois ring is constructed within a finite local ring by means of a Teichmuller representation system. Part II presents some variants of the Reed-Muller codes. Part III gives a standard basis for a linear code over a prime field. A decoding algorithm for binary linear codes using a Groebner basis is developed.
Autorenporträt
Harinaivo Andriatahiny is presently Doctor-HDR of Mathematics at the University of Antananarivo in Madagascar. His main research interests include applied algebra and coding theory.