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Conditions

Coding theory

Subject of the group A for: Informatics, Telecommunications, Electronics
Term: winter
Extent: 3-1
Year: 1st graduate study.
Lecturer: doc. RNDr. Ladislav Satko, CSc.

Proportion of final exams in the course completion: 60%.

Keywords: Fixed and variable -length codes, linear codes, error detecting codes, error correcting codes.

Annotation: An introduction to fixed and variable -length codes,error detection and correction codes, Hamming's, Golay's, Reed-Muller's codes. Cyclic and BCH codes. Syndrom cryptosystem.

Syllabus - in twelve points

  1. Fixed-length codes.
  2. Variable-length codes. Huffman method.
  3. Structure of efficient codes.
  4. Foundation of algebraic theory of linear spaces and finite groups.
  5. Finite fields calculus.
  6. Theory of error detecting and error correcting codes.
  7. Linear codes. Cosets according to a linear code. Standard decoding. Decoding with syndroms. Syndrom cryptosystem.
  8. Golay's code. Constructions and transformations of codes.
  9. Selected parts of Boolean algebras. Reed-Muller's codes.
  10. Cyclic codes. Matrix description of cyclic codes.
  11. Definition of BCH codes.
  12. Decoding of BCH codes.

Target: This is a self-contained introductory course of Coding Theory. Except of basic review of discrete probability theory we treat an introduction to fixed and variable -length codes, error detection and correction codes, Hamming's, Golay's, Reed-Muller's codes. Cyclic and BCH codes. One application to cryptology is included, too.

Recommended prerequisites: Linear algebra. Probability theory.

Bibliography:

foreign:
R.E.Blahut: Theory and Practice of Error Control Codes. Addison-Wesley Pub.Comp., 1984.
R. Gallager: Information Theory and reliable communication. J. Wiley and Sons, Inc., 1968.
available in Slovak or Czech:
O. Grošek, P. Volauf: Stochastic Processes and Information Theory. Lecture Notes, University Pub., 1990.