Cayley-Bacharach and evaluation codes on complete intersections

Details Cayley-Bacharach and evaluation codes on complete intersections Cayley-Bacharach and evaluation codes on complete intersections

2003-11-09

arxiv.org/abs/math/0311129v2

J. Pure Applied Algebra 196 (2005) 91-99

Mathematics

Algebraic Geometry

10 pages. v2: minor expository changes

Scientific paper

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.

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