Seminar in Coding Theory -- Spring 1997

Communication of information often takes place over noisy channels. That noise can introduce errors in messages sent over the channel. This is the case for instance in transmission of pictures from deep-space exploration craft like the Voyagers, in the transfer of digital information within computer systems, and in the process of storing information (music, images, etc.) on compact disks, digital audio tape, or other media, and retrieving it for use at a later time. In these situations, for reliability of communication, it is necessary to encode the transmitted information in such a way that errors can be detected and/or corrected when they occur. Designing coding schemes that achieve error control without introducing undue redundancy, and that admit efficient encoding and decoding, is the main goal of coding theory. In this course we studied:
  1. Binary block codes, the Hamming metric, error detection and correction
  2. Linear codes
  3. Syndrome decoding
  4. The Hamming and Golay codes
  5. The polynomial ring in one variable over a field
  6. Construction of general finite fields
  7. BCH and Reed-Solomon codes
  8. Polynomial division encoding
  9. The generalized Euclidean algorithm decoder for binary BCH codes
Text: Pretzel, Error-Correcting Codes and Finite Fields
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