Abstract
In the study of quantum error-correcting codes, stabilizer codes is perhaps the most important ones and can be constructed by classical self-orthogonal codes. In this thesis, our aim is to pursue a further study of the structure of quantum stabilizer codes based on syndrome assignment by classical parity check matrices. We proposed a construction by using two cyclic codes. We also found the normalizer of quantum quadratic-residue codes, which helps nd the minimum distance. Finally, a construction of [[n; k]] quantum stabilizer codes with k > 1 was proposed.