Theory of linear and integer programming
Theory of linear and integer programming
Total dual integrality implies local strong unimodularity
Mathematical Programming: Series A and B
The parameters of projective Reed-Mu¨ller codes
Discrete Mathematics
Computational methods in commutative algebra and algebraic geometry
Computational methods in commutative algebra and algebraic geometry
Combinatorics, Probability and Computing
Algebraic Geometric Codes: Basic Notions
Algebraic Geometric Codes: Basic Notions
Reed-Muller-Type Codes Over the Segre Variety
Finite Fields and Their Applications
Designs, Codes and Cryptography
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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.