University of IsfahanTransactions on Combinatorics2251-86575220160601Recursive construction of $(J,L)$ QC LDPC codes with girth 61122843010.22108/toc.2016.8430ENMohammad GholamiShahrekord University0000-0002-3174-0138Zahra RahimiUniversity of Shahrekord,Journal Article20140527In 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.http://toc.ui.ac.ir/article_8430_4d65fe9a28acc359f137574e8342c0f4.pdf