Several Explicit Constructions for (3,L) QC-LDPC Codes with Girth at Least Eight

Some explicit constructions for exponent matrices which correspond to Tanner graphs with girth at least eight are proposed. From these results, for any row weight of L>3, (3,L) quasi-cyclic LDPC codes with girth at least eight are constructed for any circulant permutation matrix (CPM) size P>L(L+mod(L,2))/2.