Cayley-Bacharach and evaluation codes on complete intersections

Leah Gold, John Little, Hal Schenck

Research output: Contribution to journalArticlepeer-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 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).

Original languageEnglish (US)
Pages (from-to)91-99
Number of pages9
JournalJournal of Pure and Applied Algebra
Volume196
Issue number1
DOIs
StatePublished - Mar 2005

ASJC Scopus subject areas

  • Algebra and Number Theory

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