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On quadratic residue codes and hyperelliptic curves
Discrete Mathematics and Theoretical Computer Science DMTCS
For an odd prime p and each non-empty subset S ⊂ GF (p), consider the hyperelliptic curve XS defined by . Using a connection between binary quadratic residue codes and hyperelliptic curves over GF (p), this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S ⊂ GF (p) for which the bound |XS(GF (p))| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct anfatcat:5zhueub5efdivmv2cd2rsm4ugm