Cayley-Bacharach and evaluation codes on complete intersections
Leah Gold, John Little, Hal Schenck
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 P2 to Pm; 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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