Details:
Title  Gr\"obner bases over commutative rings and applications to coding theory.  Author(s)  Eimear Byrne, Teo Mora  Type  Book, Chapter in Book, Conference Proceeding  Abstract  We 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) Szekereslike bases. We give an account of a number of decoding algorithms for alternant codes over commutative finite chain rings.  Keywords  Commutative rings, Finite chain rings, Galois ring, Gröbner bases  ISBN  9783540938057/hbk; 97835 
URL 
http://link.springer.com/chapter/10.1007%2F9783540938064_14 
Language  English  Pages  239261  Publisher  Berlin: Springer  Year  2009  Edition  0  Translation 
No  Refereed 
No 
