Cayley-Bacharach and evaluation codes on complete intersections
Algebraic Geometry
2007-07-16 v2 Information Theory
Commutative Algebra
math.IT
Abstract
In recent work, J. Hansen uses cohomological methods to find a lower bound for the minimum distance of an evaluation code determined by a reduced complete intersection in the projective plane. In this paper, we generalize Hansen's results from P^2 to P^m; we also show that the hypotheses in Hansen's work may be weakened. The proof is succinct and follows by combining the Cayley-Bacharach theorem and bounds on evaluation codes obtained from reduced zero-schemes.
Keywords
Cite
@article{arxiv.math/0311129,
title = {Cayley-Bacharach and evaluation codes on complete intersections},
author = {Leah Gold and John Little and Hal Schenck},
journal= {arXiv preprint arXiv:math/0311129},
year = {2007}
}
Comments
10 pages. v2: minor expository changes