Cayley-Bacharach and evaluation codes on complete intersections

Hansen (Appl. Algebra Eng. Comm. Comput. 14 (2003) 175) uses cohomological methods to find a lower bound for the minimum distance of an evaluation code determined by a reduced complete intersection in p(2). In this paper, we generalize Hansen's results from p(2) to P-m; we also show that the hypotheses of Hansen (2003) may be weakened. The proof is succinct and follows by combining the Cayley-Bacharach Theorem and the bounds on evaluation codes obtained in Hansen (Zero-Dimensional Schemes (Ravello, 1992), de Gruyter, Berlin, 1994, pp. 205-211). (C) 2004 Elsevier B.V. All rights reserved.