Details:
Title  Applying Buchberger  Author(s)  Parisa Alvandi, Amir Hashemi  Type  Article in Journal  Abstract  Norton and Sălăgean [Strong Gröbner bases and cyclic codes over a finitechain ring, in Proc. Workshop on Coding and Cryptography, Paris, Electronic Notes in Discrete Mathematics, Vol. 6 (Elsevier Science, 2001), pp. 391–401] have presented an algorithm for computing Gröbner bases over finitechain rings. Byrne and Fitzpatrick [Gröbner bases over Galois rings with an application to decoding alternant codes, J. Symbolic Comput.31 (2001) 565–584] have simultaneously proposed a similar algorithm for computing Gröbner bases over Galois rings (a special kind of finitechain rings). However, they have not incorporated Buchberger's criteria into their algorithms to avoid unnecessary reductions. In this paper, we propose the adapted version of these criteria for polynomials over finitechain rings and we show how to apply them on Norton–Sălăgean algorithm. The described algorithm has been implemented in Maple and experimented with a number of examples for the Galois rings.
 Keywords  Gröbner bases; Buchberger's algorithm; Buchberger's criteria; finitechain rings  ISSN  02194988 
URL 
http://www.worldscientific.com/doi/abs/10.1142/S0219498813500345 
Language  English  Journal  J. Algebra Appl.  Volume  12  Number  7  Pages  15  Publisher  World Scientific, Singapore  Year  2013  Edition  0  Translation 
No  Refereed 
No 
