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Presents a new hardware decoder for double-error-correcting binary BCH codes of primitive length, based on a modified step-by-step decoding algorithm. This decoding algorithm can be easily implemented with VLSI circuits. As the clock rate of the decoder is independent of block length and is only twice the data rate, the decoder is suitable for long block codes working at high data rates. The decoder comprises a syndrome calculation circuit, a comparison circuit and a decision circuit, which can be realised by linear feedback shift registers, ROMs and logical gates. The decoding algorithm, circuit design and data processing sequence are described in detail. The circuit complexity, decoding speed and data rate of the new decoder are also discussed and compared with other decoding methods.