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BCH Codes

11.1  Binary BCH Codes

The BCH codes are named after Bose-Chaudhuri-Hocquebghem (Bose and Chaudhuri [1960], and Hocquenghem [1959]). These codes are multiple error correcting codes and are a generalization of the Hamming codes. Because of their high coding rate, they have inspired a lot of study to find fast hardware encoding and decoding schemes and to develop their applications in high-speed memory.

Recall that the Hamming (n, k) codes with m = n – k parity-check bits have the following characteristics: Block length: n = 2m − 1; data bits: k = 2m – m − 1; and correctable errors: t = 1. The Golay codes are the other classes of codes that are more versatile than the Hamming codes; their minimum distance is 7, so they can correct ...

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