Quasi-Quadratic Residue Codes and their weight distributions

Quasi-Quadratic Residue Codes (QQR Codes) are a family of double circulant codes. They are important in at least two respects: Firstly, they have very good minimum distances when p ≡ 3 (mod 8), providing a critical test case for Goppa's Conjecture. Secondly, they serve as a powerful tool for studying point distributions on hyperelliptic curves. We will use the result of their weight distributions to prove a variant on a result of Larsen [1] on asymptotic normal distribution of numbers of points on hyperelliptic curves.