  In this paper, a construction of a pair of "regular" quasi-cyclic LDPC codes
as ingredient codes for a quantum error-correcting code is proposed. That is,
we find quantum regular LDPC codes with various weight distributions.
Furthermore our proposed codes have lots of variations for length, code rate.
These codes are obtained by a descrete mathematical characterization for model
matrices of quasi-cyclic LDPC codes.
  Our proposed codes achieve a bounded distance decoding (BDD) bound, or known
as VG bound, and achieve a lower bound of the code length.
