Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Computer Science
- Code
- kodszi1u0um17em
- Title
- Codes and symmetric structures (l)
- Usual semester
- Autumn
- ECTS
- 3
- Language
- en
- Learning outcomes
- Knowledge: getting familiar with the codes and symmetric structures Ability: to understand and use codes and symmetric structures Attitude: the need to extend the mathematical knowledge, to gain new analytic skills Autonomy and Responsibility: based on the gained knowledge in codes and symmetric structures, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Error correcting codes: Hamming, BCH (Bose, Ray-Chaudhuri, Hocquenheim) codes. Bounds on code parameters: Hamming bound and perfect codes, Singleton bound and MDS codes. Reed-Solomon, Reed-Muller codes. The Gilbert-Varshamov bound. Random codes, explicit asymptotically good codes (Forney's concatenated codes, Justesen codes). Block systems, t-systems and their relationship with perfect codes. Binary and ternary Golay codes and Witt block systems. Fisher's inequality and its variants. Square block systems, the Bose-Chowla-Ryser necessary condition for their existence. Recursive and direct constructions for block systems.
- Assessment method
- exam
- Bibliography
- lecture notes