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TitleApplying Buchberger
Author(s) Parisa Alvandi, Amir Hashemi
TypeArticle in Journal
AbstractNorton and Sălăgean [Strong Gröbner bases and cyclic codes over a finite-chain 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 finite-chain 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 finite-chain 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 finite-chain 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.

KeywordsGröbner bases; Buchberger's algorithm; Buchberger's criteria; finite-chain rings
URL http://www.worldscientific.com/doi/abs/10.1142/S0219498813500345
JournalJ. Algebra Appl.
PublisherWorld Scientific, Singapore
Translation No
Refereed No