This course is to introduce basic notions in the theory of error-correcting codes which is used in data storage and telecommunication.
* Error detection, correction and decoding, Hamming distance
* Basic facts on finite fields
* Linear codes, Hamming weight, generator and parity-check matrices, encoding, decoding.
* Bounds, Hamming codes, Golay codes, perfect codes, MDS codes
* Construction of codes, Reed-Muller codes.
* Cyclic codes, generator polynomials, BCH codes, Reed-Solomon codes
* Computer implementation of efficient coding and decoding.
Programme: MATH(SPS)
This course is to introduce basic notions in the theory of error-correcting codes which is used in data storage and telecommunication. * Error detection, correction and decoding, Hamming distance * Basic facts on finite fields * Linear codes, Hamming weight, generator and parity-check matrices, encoding, decoding. * Bounds, Hamming codes, Golay codes, perfect codes, MDS codes * Construction of codes, Reed-Muller codes. * Cyclic codes, generator polynomials, BCH codes, Reed-Solomon codes * Computer implementation of efficient coding and decoding.