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This paper presents an approach to the construction of low-density parity-check (LDPC) codes based on hyperplanes (mu-flats) of different dimensions in Euclidean geometries. Codes constructed by this method have quasicyclic and irregular structure. The degree distributions of these codes are optimized by the curve fitting approach in the extrinsic information transfer (EXIT) charts. By constraining the fraction of degree-2 nodes, we can lower the error floor at the cost of a small increase in the threshold SNR. Simulation results show that these codes perform very well at both of waterfall region and the error floor region with the iterative decoding.