Abstract: A family of special quantum stabilizer codes is defined with the property that in the stabilizer all phases are 1 and the part of bit-flip is cyclic, which includes well-known CSS codes. Its encoding and decoding are present. The encoding process needs an encoded 0 state to begin with. Then any encoded state can be obtained by control of the logical state. Decoding could be performed by running the encoding process backwards with the output of the encoded 0 state besides the desired logical state. This encoded 0 state can be used in the next encoding directly, which simplifies encoding and decoding greatly because the complexity of this method lies in producing the encoded 0 state. These processes possess a highly regular structure.

Key words: quantum information, encoding and decoding, encoded 0 state, quantum stabilizer codes