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In this brief, a shuffled schedule (SS) of the min-max decoding algorithm is proposed for nonbinary low-density parity-check (LDPC) codes. To increase the throughput and reduce the memory requirement, a modified SS (MSS) with much simpler check node processing is also proposed, based on a new shuffled merge algorithm. Numerical simulations for three LDPC codes with different lengths and rates over GF(32) show: 1) both SS and MSS converge faster and have slightly better error performance than the flooding schedule, and 2) the degradation of the MSS in error performance as well as convergence rate is negligible. Finally, an efficient decoder architecture based on the MSS is proposed for quasi-cyclic LDPC codes. The proposed decoder architecture further enhances the decoding throughput with improved check and variable node processing units. The implementation results of an (837, 726) LDPC decoder over GF(32) demonstrate that the proposed architecture outperforms those in previous works.