University of Isfahan Transactions on Combinatorics 2251-8657 5 2 2016 06 01 Recursive construction of $(J,L)$ QC LDPC codes with girth 6 11 22 8430 10.22108/toc.2016.8430 EN Mohammad Gholami Shahrekord University Zahra Rahimi University of Shahrekord, Journal Article 2014 05 27 ‎In this paper‎, ‎a recursive algorithm is presented to generate some exponent matrices which correspond to Tanner graphs with girth at least 6‎. ‎For a $J \times L$ exponent matrix $E$‎, ‎the lower bound $Q(E)$ is obtained explicitly such that $(J,L)$ QC LDPC codes with girth at least 6 exist for any circulant permutation matrix (CPM) size $m \geq Q(E)$‎. ‎The results show that the exponent matrices constructed with our recursive algorithm have smaller lower-bound than the ones proposed recently with girth 6‎. https://toc.ui.ac.ir/article_8430_4d65fe9a28acc359f137574e8342c0f4.pdf