  For an arbitrary (3,L) QC-LDPC code with a girth of twelve, a tight lower
bound of the consecutive lengths is proposed. For an arbitrary length above the
bound the resultant code necessarily has a girth of twelve, and for the length
meeting the bound, the corresponding code inevitably has a girth smaller than
twelve. The conclusion can play an important role in the proofs of the
existence of large-girth QC-LDPC codes, the construction of large-girth QC-LDPC
codes based on the Chinese remainder theorem, and the construction of LDPC
codes with the guaranteed error correction capability.
