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In this paper,we consider the performance-optimized non-binary LDPC(low density parity check)code over general linear group,(C).A new methodology for constructing the binary representation(generalized binary representation,GBR)of(C)is proposed which can be optimized with regard to both degree distributions and girth.As to the decoding of the GBR,we develop a low complexity hybrid parallel decoding process.It is shown that the decoding performance of the GBR under the proposed binary decoding process could closely approach the decoding performance of its mother code(C)under non-binary BP(belief propagation)decoding.A simple code optimization algorithm for the GBR is also provided.Simulations show the comparative results and justify the advantages of the proposed constructions.