IJPAM: Volume 78, No. 3 (2012)

EVALUATION CODES ALONG SUBSETS
OF COMPLETE INTERSECTIONS

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract. Fix a zero-dimensional scheme $E\subset \mathbb {P}^r$ defined over the finite field $K$. For any $S\subseteq \mathbb {P}^r(K)$ such that $S\cap E=\emptyset$ let $\mathcal {C}(S,m,E)$ denote the evaluation code obtained evaluating $H^0(\mathbb {P}^r,\mathcal {I}_E(m)))$ at the points of $S$. Here we extend works of Hansen, (case $E=\emptyset$) to the case of a complete intersections $E\cup S$. The proofs for the minimum distance are the same.

Received: December 13, 2011

AMS Subject Classification: 14N05, 16E65, 94B27

Key Words and Phrases: evaluation code, complete intersection, Gorenstein zero-dimensional scheme

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 3