Construction of quantum codes based on elementary transformations

To investigate the general technique for simply constructing quantum stabilizer code, when the conditions of the dual constraints (C⊥⊆C) are met, a new constructing method based on elementary transformations is put forward, by which a class of quantum stabilizer codes C′=[[N-1, K+1, D′]]q can be constructed from another class of quantum stabilizer codes C=[[N, K, D]]q with C⊥⊆C. In the codes structure, quantum stabilizer codes and classical error correction codes operate on the same field Fq, eliminating the conversion from Fq2 to Fq and complicated mathematical operations. Using only the concepts of inner product space and elementary row transformation matrix, a class of derivative code of the codes can be constructed, and the efficiency of time and space of the algorithm can be improved. Constructive proof of the method is simple and easy to understand. In addition, the code construction and check are easy to implement, especially applicable to computer. Theoretical results show that the method is helpful for the construction of a class of quantum codes.