F. Amirzade - Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.
M. Alishahi - Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.
M.R. Rafsanjani-Sadeghi - Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.

In this paper, we define a structure to obtain exponent matrices of girth-8 QC-LDPC codes with column weight 3. Using the difference matrices introduced by Amirzade et al., we investigate necessary and sufficient conditions which result in a Tanner graph with girth 8. Our proposed method contributes to reduce the search space in recognizing the elements of an exponent matrix. In fact, in this method we only search to obtain one row of an exponent matrix. The other rows are multiplications of that row.

QC-LDPC codes, girth, Difference matrices, Lifting degree