Details:
Title  Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields  Author(s)  Rosales José Carlos, Aron Simis, Rafael H. Villarreal  Type  Article in Journal  Abstract  Let 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 nonbipartite, we show an upper bound for the minimum distance.  Keywords  Projective variety, Degree, Index of regularity, Hilbert function, Minimum distance  ISSN  10715797 
URL 
http://www.sciencedirect.com/science/article/pii/S1071579710000754 
Language  English  Journal  Finite Fields and Their Applications  Volume  17  Number  1  Pages  81  104  Year  2011  Edition  0  Translation 
No  Refereed 
No 
