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In this paper we propose a semi-random technique to design irregular LDPC codes with low error floor. In particular, the suggested technique is related to a popular class of irregular LDPC codes that can be encoded in linear time, and tries to avoid both low-weight codewords and near-codewords, which limit the performance of the belief propagation decoder. Besides, an easy and effective rule to design puncturing patterns for this class of LDPC codes is provided. The effectiveness of the new design criteria is proved by comparison with literature results.