APPLYING BUCHBERGER%26apos;S CRITERIA FOR COMPUTING GROBNER BASES OVER FINITE-CHAIN RINGS

作者：Hashemi Amir^*; Alvandi Parisa

来源：Journal of Algebra and Its Applications, 2013, 12(7): 1350034.

DOI：10.1142/S0219498813500345

• Grobner bases
• Buchberger%26apos
• s algorithm
• Buchberger%26apos
• s criteria
• finite-chain rings

Norton and Salagean [Strong Grobner 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 Grobner bases over finite-chain rings. Byrne and Fitzpatrick [Grobner 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 Grobner bases over Galois rings (a special kind of finite-chain rings). However, they have not incorporated Buchberger%26apos;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-Salagean algorithm. The described algorithm has been implemented in Maple and experimented with a number of examples for the Galois rings.

• 出版日期2013-11