%0 Journal Article
%T On quadratic residue codes and hyperelliptic curves
%A David Joyner
%J Discrete Mathematics & Theoretical Computer Science
%D 2008
%I Discrete Mathematics & Theoretical Computer Science
%X For an odd prime p and each non-empty subset S GF(p), consider the hyperelliptic curve X S defined by y 2 =f S (x), where f S (x) = ¡Ç a¡ÊS (x-a). 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 |X S (GF(p))| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''
%U http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/606