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Reed-Muller code is a kind of decomposable code which can be decoded with multi-stage decoding. In this paper, we first analyze the theory of Reed-Muller coding and introduce a decoding Reed algorithm, which can recover information from received codes without obvious computation of syndrome. An improved Reed decoding algorithm is proposed, which can greatly reduce the complexity of producing a checksum. DSP implementation of a Reed-Muller codec is then presented.