Enabling the parity-check matrices to have a large girth is an efficient method to improve the decoding performance for many binary and non-binary QC-LDPC codes.A new explicit framework to construct QC-LDPC codes with girth at least eight is proposed

without any computer search procedures.The QC-LDPC codes constructed by the framework not only have a girth at least eight

but also possess an advantage of consecutive cyclic permutation matrix (CPM) sizes.The framework includes two steps:first

a parity-check matrix is explicitly constructed with a girth at least eight under an infinite CPM size;second

the tight lower bound of consecutive CPM sizes is precisely calculated directly from the corresponding shift matrix of the parity-check matrix

by employing a new girth property discovered by this paper.