On quadratic residue codes and hyperelliptic curves

Details On quadratic residue codes and hyperelliptic curves On quadratic residue codes and hyperelliptic curves

2006-09-20

arxiv.org/abs/math/0609562v2

Mathematics

Combinatorics

18 pages, no figures

Scientific paper

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?

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