Details:
| Title | Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields | | Author(s) | 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 non-bipartite, we show an upper bound for the minimum distance. | | Keywords | Projective variety, Degree, Index of regularity, Hilbert function, Minimum distance | | ISSN | 1071-5797 |
| 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 |
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