Cayley-Bacharach and evaluation codes on complete intersections

Leah Gold; John Little; Hal Schenck

doi:10.1016/j.jpaa.2004.08.015

Cayley-Bacharach and evaluation codes on complete intersections

Leah Gold
, John Little
, Hal Schenck

Research output: Contribution to journal › Article › peer-review

Abstract

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 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).

Original language	English (US)
Pages (from-to)	91-99
Number of pages	9
Journal	Journal of Pure and Applied Algebra
Volume	196
Issue number	1
DOIs	https://doi.org/10.1016/j.jpaa.2004.08.015
State	Published - Mar 2005
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2004.08.015

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title = "Cayley-Bacharach and evaluation codes on complete intersections",

abstract = "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).",

author = "Leah Gold and John Little and Hal Schenck",

note = "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.",

year = "2005",

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doi = "10.1016/j.jpaa.2004.08.015",

language = "English (US)",

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journal = "Journal of Pure and Applied Algebra",

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T1 - Cayley-Bacharach and evaluation codes on complete intersections

AU - Gold, Leah

AU - Little, John

AU - Schenck, Hal

N1 - 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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Cayley-Bacharach and evaluation codes on complete intersections

Abstract

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