TY - JOUR
T1 - Cayley-Bacharach and evaluation codes on complete intersections
AU - Gold, Leah
AU - Little, John
AU - Schenck, Hal
N1 - Funding Information:
This collaboration began while the authors were members of MSRI. We also thank the Institute for Scientific Computation at Texas A&M for providing logistical support. Gold is partially supported by an NSF-VIGRE postdoctoral fellowship. Schenck is partially supported by NSF grant 03-11142. NSA grant MDA 904-03-1-0006 and ATP grant 010366-0103.
PY - 2005/3
Y1 - 2005/3
N2 - 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 ℙ2. In this paper, we generalize Hansen's results from ℙ2 to ℙm; 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).
AB - 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 ℙ2. In this paper, we generalize Hansen's results from ℙ2 to ℙm; 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).
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U2 - 10.1016/j.jpaa.2004.08.015
DO - 10.1016/j.jpaa.2004.08.015
M3 - Article
AN - SCOPUS:10644231655
VL - 196
SP - 91
EP - 99
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 1
ER -