The submatrix of Hc is used to correct Pauli X errors, and the submatrix of Hd to correct Pauli Z errors.
Using submatrices obtained from Hc and Hd by deleting rows, we can alter the code rate. Two distinct, orthogonal matrices Hc and Hd are used. Manabu Hagiwara et al., 2007 presented a method to calculate parity check matrices with high girth. Quasi- cyclic LDPC codes can approach the Shannon capacity and have efficient decoders. Jing, Lin Brun, Todd Quantum Research Team Error Correction using Quantum Quasi- Cyclic Low-Density Parity-Check(LDPC) Codes
