Study Of Several Problems In Theory Of Quantum Error-Correcting Codes

Quantum computer has interested people greatly for its remarkable computation capacity. However, to make quantum computer practical, it is necessary to find the effective method to win through decoherence. Quantum error-correcting code is one of good methods to get over decoherence.This dissertation focuses on the study of several problems in the theory of quantum error-correcting codes. By the connection between quantum codes and classical codes, quantum constacyclic codes are constructed based on classical constacyclic codes. In the meantime, some new quantum Hamming codes are found. A class of quantum MDS codes, quantum generalized Reed-Solomon codes, is derived from classical generalized Reed-Solomon codes. Moreover, a unified framework of quantum MDS codes is given. Quantum code concatenation structure is presented, based on which a family of asymptotically good quantum codes is constructed. From classical Justesen codes, quantum Justesen codes are obtained with the property that this is the first time that good quantum codes are derived from bad quantum codes.