Transform Techniques for Error Control Codes

R. E. Blahut
1979 IBM Journal of Research and Development  
By using the theory ofjinite5eld Fourier transforms, the subject o f error control codes is described in N language familiar to thejield of signal processing. The many importunt uses of spectral techniques in error control are summarized. Many classes of linear codes are given a spectral interpretation and some new codes are described, Several nlternative encoder1 decoder schemes are described by frequency domclin reasoning. In particular, an errors-and-erasures decoderjor a BCH code is
more » ... d which has virtuully no additional computations over an errors-only decoder. Techniques for decoding BCH, R S , and alternant codes (Goppa codes) a short distance beyond the designed distance ure discussed. Also, (4 modijication to the definition of a BCH code is described which reduces the decoder complexity without changing the code's rute or minimum distance. We then turn from the tutorial tone to give some new techniques. The spectral interpretation is used to describe encoderidecoder implementations for BCH and Reed-
doi:10.1147/rd.233.0299 fatcat:txfqsqdsezak7ldzi73ckotuze