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TitleAlgebraic methods for parameterized codes and invariants of vanishing ideals over finite fields
Author(s) Rosales José Carlos, Aron Simis, Rafael H. Villarreal
TypeArticle in Journal
AbstractLet K = F q be a finite field with q elements and let X be a subset of a projective space P s − 1 , over the field K, parameterized by Laurent monomials. Let I ( X ) be the vanishing ideal of X. Some of the main contributions of this paper are in determining the structure of I ( X ) to compute some of its invariants. It is shown that I ( X ) is a lattice ideal. We introduce the notion of a parameterized code arising from X and present algebraic methods to compute and study its dimension, length and minimum distance. For a parameterized code, arising from a connected graph, we are able to compute its length and to make our results more precise. If the graph is non-bipartite, we show an upper bound for the minimum distance.
KeywordsProjective variety, Degree, Index of regularity, Hilbert function, Minimum distance
URL http://www.sciencedirect.com/science/article/pii/S1071579710000754
JournalFinite Fields and Their Applications
Pages81 - 104
Translation No
Refereed No