Quadratic forms, generalized Hamming weights of codes and curves with many points
type: Item
instance of: scholarly article
title: Quadratic forms, generalized Hamming weights of codes and curves with many points
zbMATH Open document ID: 0872.94052
author: Gerard van der Geer
author: Marcel van der Vlugt
published in: Journal of Number Theory
publication date: 1997-09-30T00:00:00Z
full work available at URL: quadratic-forms-generalized-hamming-weights-of-codes-and-curves-with-many-points(62a9bc6d-8036-4bc3-98d3-ae4e21674228).html
review text: The paper under review continues the series of the authors' papers [Compos. Math. 84, 333--367 (1992; Zbl 0804.14014), Combin. Theory Ser. A 70, 337--348 (1995; Zbl 0824.94025)]. The main idea is in an interplay between binary trace codes, quadratic forms over \(\mathbb F_2\), and fibre products of Artin-Schreier curves. The authors construct subcodes in trace codes consisting of minimum weight words. This allows them to obtain curves with many rational points. Namely, for certain genera they improve known lower bounds for the maximal number of rational points and exhibit some curves attaining the Hasse-Weil upper bound.
Mathematics Subject Classification ID: 94B27
Mathematics Subject Classification ID: 11G20
Mathematics Subject Classification ID: 14G50
zbMATH DE Number: 913829
zbMATH Keywords: binary trace codes
zbMATH Keywords: quadratic forms
zbMATH Keywords: Artin-Schreier curves
reviewed by: Boris Kunyavskiĭ
MaRDI profile type: Publication
OpenAlex ID: W2084882420
DOI: 10.1006/JNTH.1996.0086
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description: scientific article; zbMATH DE number 913829