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In an earlier paper, we reported that the low-density parity-check (LDPC) codes from finite planes outperform any other known forward error-correction (FEC) scheme for optical communications. However, the number of different LDPC codes of code rate above 0.8 is rather small. As a natural extension of the prior work, in this paper, we consider LDPC codes on m flats derived from projective and affine geometries, which outperform codes from finite planes. The codes on m flats also provide a greater selection of structured LDPC codes of rate 0.8 or higher. The performance of the codes in a long-haul optical-communication system was assessed using an advanced simulator able to capture all important transmission impairments. Specifically, they achieve a coding gain of 10 dB at a bit error rate (BER) of 10-9, outperforming, therefore, the best turbo product codes proposed for optical communications. In addition, the simulator implements a fixed-point (FP) iterative decoder that allows control of the precision of the soft information used in the decoder. Such quantization is required to facilitate hardware implementations of the iterative decoder, and the high-speed operations for long-haul optical transmission systems. The loss in performance due to reduced precision of the soft information can be as low as 0.2 dB.