A method to design a parity-check matrix with a generalized anti-Pasch configuration is developed for a self-orthogonal quasi-cyclic code as a regular low-density parity-check code. This method can be applied to search a parity-check matrix with an arbitrary constant column weight and with an arbitrary number of rows. The minimum Hamming distance of a code designed by this method is at least the column weight plus two for an even column weight and the column weight plus three for an odd column weight. It is shown that the error floor and undetected error probabilities of a code with a high code rate above 0.95 designed by this method are significantly improved compared with those of a conventional self-orthogonal quasi-cyclic code based on finite geometry.
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