Mathematics BSc
Course description
2013.
Course description
2013.
Algebraic coding theory
Hours lect+pc |
Credits lect+pc |
Assessment | Specialization | Course code lect/pc |
Semester | Status |
---|---|---|---|---|---|---|
2 + 0 | 2 + 0 | exam | applied math. | mm1c1ak6e | 6 | recommended |
Course coordinator
Strong | Weak | Prerequisites | |
---|---|---|---|
Lecture | |||
Strong:
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Prerequisites
Classical and linear algebra, finite fields.
Course objectives
Introduction to the basic methods of
error-correcting codes, an important application of abstract
algebra.
Literature
- E. R. Berlekamp: Algebraic Coding Theory. Aegean Park Pr; 1984.
Syllabus
- Basic notions: Noisy channels, binary symmetric channel, error detection and error correction.
- Block codes. Hamming distance, minimal distance.
- Algebraic tools: finite fields (basic properties, existence and uniqueness, constructions, polynomials over finite fields).
- Linear codes, generator and parity check matrices, Hamming codes.
- Cyclic codes, described by means of ideals.
- Codes and polynomials: generating and parity check polynomials, BCH codes, Reed-Solomon codes, quadratic residue codes, Reed-Muller codes, Golay codes, perfect codes.
- Bounds on linear codes: Singleton, Hamming, Gilbert-Varshamov, Plotkin.
- Decoding methods: syndromes, decoding BCH codes.
- Error correction in digital media processing (compact disc).