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Low density parity check (LDPC) codes over GF(2m) are an extension of binary LDPC codes with significantly higher performance. However, the computational complexity of the encoders/decoders for these codes is also higher. Hence there is a substantial lack of hardware implementations for LDPC over GF(2m) codes. This paper proposes a novel variation of the belief propagation algorithm for GF(2m) LDPC codes. The new algorithm results in a reduced hardware complexity when implemented in VLSI. The serial architecture of the novel decoding algorithm and two other algorithms for LDPC over GF(2m) are implemented on an FPGA. The results show that the proposed algorithm has substantial advantages over existing methods. We show that the implementation of LDPC over GF(2m) decoder is feasible for short to medium length codes. The additional complexity of the decoder is balanced by the superior performance of GF(2m) LDPC codes.