IJPAM: Volume 97, No. 2 (2014)
DUALS OF ALGEBRAIC-GEOMETRIC CODES
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
Abstract. Here we extends a work of A. Couvreur on the Hamming distance of the dual of an evaluation code to its generalized Hamming weights. We prove the following result.
Fix integers , and . Let be a zero-dimensional scheme such that . If assume that spans and that the sum of the degrees of the non-reduced connected components of is at most . We have if and only if there is as one of the schemes in the following list:
- and is contained in a line;
- and is contained in a reduced plane conic;
- , , and there are an integer and lines , such that , and .
Received: August 6, 2014
AMS Subject Classification: 4N05, 14Q05, 94B27
Key Words and Phrases: dual code, generalized Hamming weights, higher support weights, evaluation code, plane curve, algebraic-geometric code
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DOI: 10.12732/ijpam.v97i2.13 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 241 - 251