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TitleA new algorithm for an $S$-polynomial.
Author(s) Jinwang Liu, Licui Zheng
TypeArticle in Journal
AbstractThe authors study affine codes parametrised by monomials and their projective form. The main point is to compute the dimension, the length and the minimum distance of these codes using Gr\"{o}bner bases. It is shown that these basic parameters coincide for the affine and the projective form of such a code and that the first two parameters can be expressed in terms of the Hilbert function and the degree of the homogeneous vanishing ideal. In particular, the basic parameters are computed for the case that the code comes from an affine torus. Finally, the authors present an implementation of their results in Macaulay 2.
KeywordsGröbner basis; GVW algorithm; S-polynomial
ISSN1000-0577
LanguageEnglish
JournalJ. Syst. Sci. Math. Sci.
Volume32
Number8
Pages950--956
PublisherScience Press, Beijing
Year2012
Edition0
Translation No
Refereed No
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