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 image. In this paper, we generalize Hansenʹs results from image to image; 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).