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中文摘要：
对于围长为12的任意（3,L）QC-LDPC码,提出了连续码长的紧致下界.当码长大于下界时围长必然为12,当码长等于下界时围长必然小于12.本文研究结论对于大围长QC-LDPC码的存在性研究、基于中国剩余定理的大围长QC-LDPC码构造、具有纠错能力保证的LDPC码构造等问题具有重要应用价值.
英文摘要：
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.
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