On quadratic residue codes and hyperelliptic curves

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A long standing problem has been to develop "good" binary linear codes to be used for error-correction. This paper investigates in some detail an attack on this problem using a connection between quadratic residue codes and hyperelliptic curves. One question which coding theory is used to attack is: Does there exist a c<2 such that, for all sufficiently large $p$ and all subsets S of GF(p), we have |X_S(GF(p))| < cp?
18 pages, no figures

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Combinatorics, Information Theory, Algebraic Geometry, Number Theory, 94B40, 11T71, 14G15, 14G50

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http://salesiana.dossiersoluciones.com/handle/123456789/155273

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0609562
 http://arxiv.org/abs/math/0609562

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arXiv