Low-density parity-check (LDPC) codes are excellent candidates for optical network applications due to their inherent low complexity of both encoders and decoders. A cyclic or quasi-cyclic form of finite geometry LDPC codes simplifies the encoding procedure. In addition, the complexity of an iterative decoder for such codes, namely the min-sum algorithm, is lower than the complexity of a turbo or Reed-Solomon decoder. In fact, simple hard-decoding algorithms such as the bit-flipping algorithm perform very well on codes from projective planes. In this paper, the authors consider LDPC codes from affine planes, projective planes, oval designs, and unitals. The bit-error-rate (BER) performance of these codes is significantly better than that of any other known foward-error correction techniques for optical communications. A coding gain of 9-10 dB at a BER of 10-9, depending on the code rate, demonstrated here is the best result reported so far. In order to assess the performance of the proposed coding schemes, a very realistic simulation model is used that takes into account in a natural way all major impairments in long-haul optical transmission such as amplified spontaneous emission noise, pulse distortion due to fiber nonlinearities, chromatic dispersion, crosstalk effects, and intersymbol interference. This approach gives a much better estimate of the code's performance than the commonly used additive white Gaussian noise channel model.