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TitleGr\"obner bases over commutative rings and applications to coding theory.
Author(s) Eimear Byrne, Teo Mora
TypeBook, Chapter in Book, Conference Proceeding
AbstractWe give a survey of results and applications relating to the theory of Gröbner bases of ideals and modules where the coefficient ring is a finite commutative ring. For applications, we specialize to the case of a finite chain ring. We discuss and compare the main algorithms that may be implemented to compute Gröbner and (in the case of a chain ring) Szekeres-like bases. We give an account of a number of decoding algorithms for alternant codes over commutative finite chain rings.
KeywordsCommutative rings, Finite chain rings, Galois ring, Gröbner bases
ISBN978-3-540-93805-7/hbk; 978-3-5
URL http://link.springer.com/chapter/10.1007%2F978-3-540-93806-4_14
LanguageEnglish
Pages239--261
PublisherBerlin: Springer
Year2009
Edition0
Translation No
Refereed No
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