In this chapter, we will give information about Bose-Chaudhuri-Hocquenghem, i.e., BCH, and Reed-Solomon codes. These codes fall into the category of linear cyclic codes. BCH codes are binary cyclic codes, and on the other hand, Reed-Solomon codes are nonbinary cyclic codes. The generator polynomials of these cyclic codes are constructed using the minimal polynomials of the extended finite fields. For this reason, it is vital to have fundamental knowledge of extended finite fields to comprehend the topics presented. In this chapter, we first explain the construction of the generator polynomials of the BCH codes using minimal polynomials of the extended fields. Using the generator polynomials, generator and parity check matrices of the BCH codes can be obtained. Next, the syndrome decoding operation of the BCH codes using error location polynomial is explained by examples. Finally, we provide information about the PGZ algorithm used for the decoding of BCH codes.

Keywords

BCH codes Generator polynomials Syndrome decoding of BCH codes PGZ algorithm Systematic encoding of BCH codes

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