Decoding RS and BCH Codes (Part 2)

  • Emilio Sanvicente


Decoding continues in this chapter by first presenting an equation known as the “key equation” that allows to treat errors and erasures in a unified manner. The formula leads to a close expression to compute the values of errata avoiding the chore of having to solve systems of linear equations. The key equation also hints the way to a different method of decoding Reed–Solomon codes based on the Euclidean algorithm that does not require the previous knowledge of the locator polynomial. The Euclidean algorithm was first used to decode Goppa codes. These codes, together with their “offspring,” the binary Goppa codes, are covered in Appendix G. The last decoding method presented in the chapter is based on the Discrete Fourier Transform (DFT) which is introduced from scratch without resorting to any previous knowledge on behalf of the reader. The method is then applied to decode not only errors but also errata.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Emilio Sanvicente
    • 1
  1. 1.Former Professor of Electrical Engineering, School of Telecommunication EngineeringPolytechnic University of CataloniaBarcelonaSpain

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