On the girth of Tanner (3,11) quasi-cyclic LDPC codes

Motivated by the works on the girth of Tanner (3,5) and (3,7) quasi-cyclic (QC) low-density parity-check (LDPC) codes done by S. Kim et al. and M. Gholami et al., respectively, we analyze the cycles of Tanner (3,11) QC LDPC codes and present the sufficient and necessary conditions for the existence of cycles of lengths 4, 6, 8, and 10 in Tanner (3,11) QC LDPC codes. By checking these conditions, the girth values of Tanner (3,11) QC LDPC codes are derived.