In this paper, we begin by reviewing some of the known properties of QQRcodes and proved that $PSL_2(p)$ acts on the extended QQR code when $p \equiv 3\pmod 4$. Using this discovery, we then showed their weight polynomials satisfya strong divisibility condition, namely that they are divisible by $(x^2 +y^2)^{d-1}$, where $d$ is the corresponding minimum distance. Using thisresult, we were able to construct an efficient algorithm to compute weightpolynomials for QQR codes and correct errors in existing results on quadraticresidue codes. In the second half, we use the relation between the weight of codewords andthe number of points on hyperelliptic curves to prove that the symmetrizeddistribution of a set of hyperelliptic curves is asymptotically normal.
展开▼
