An Improved Quantum LDPC Codes Construction Based on Balanced Incomplete Block Designs

Taking advantages of the property of classical codes from balance incomplete block designs (BIBDs), an improved construction of quantum Low Density Parity Check (quantum LDPC) codes is proposed in this paper. In the construction, we modified the original "Construction B" procedures to assure the quantum parity check matrix commutativity. It is shown that this construction method is a systematic structured method, and it is easier to obtain quantum codes. By simulation, we find the quantum parity check matrix obtained by our method are sparser than those from the method proposed by Ivan, and the codes have more good performance with the belief propagation iterative decoding algorithms.