Chapter 6BCH and Reed–Solomon Codes: Designer Cyclic Codes

The most commonly used cyclic error‐correcting codes may be the BCH and Reed–Solomon (RS) codes. The BCH code is named after Bose, Ray–Chaudhuri, and Hocquenghem (see the references at the end of the chapter), who published work in 1959 and 1960 which revealed a means of designing codes over images with a specified design distance. Decoding algorithms were then developed by Peterson and others.

The RS codes are also named after their inventors, who published them in 1960. It was later realized that RS codes and BCH codes are related and that their decoding algorithms are quite similar.

This chapter describes the construction of BCH and RS codes and several decoding algorithms. Decoding of these codes is an extremely rich area. Chapter 7 describes other “modern” decoding algorithms.

6.1 BCH Codes

 

6.1.1 Designing BCH Codes

BCH codes are cyclic codes and hence may be specified by a generator polynomial. A BCH code over images of length images capable of correcting at least images errors is specified as follows:

  1. Determine the smallest such that ...

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