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An optimization algorithm for the design of puncturing patterns for low-density parity-check codes is proposed. The algorithm is applied to the base matrix of a quasi-cyclic code, and is expanded for each block size used. Thus, storing puncturing patterns specific to each block size is not required. Using the optimization algorithm, the number of 1-step recoverable nodes in the base matrix is maximized. The obtained sequence is then used as a base to obtain longer puncturing sequences by a sequential increase of the allowed recovery delay. The proposed algorithm is compared to one previous greedy algorithm, and shows superior performance for high rates when the heuristics are applied to the base matrix in order to create block size-independent puncturing patterns.