SUBJECT
Title
Codes and symmetric structures
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Error-correcting codes; important examples: Hamming, BCH (Bose, Ray-Chaudhuri, Hocquenheim) codes. Bounds for the parameters of the code: 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 designs t-designs and their links with perfect codes. Binary and ternary Golay codes and Witt designs. Fisher's inequality and its variants. Symmetric designs, the Bruck-Chowla-Ryser condition. Constructions (both recursive and direct) of block designs.
Readings
- P.J. Cameron, J.H. van Lint: Designs, graphs, codes and their links Cambridge Univ. Press, 1991.
- J. H. van Lint: Introduction to Coding theory, Springer, 1992.
- J. H. van Lint, R.J. Wilson, A course in combinatorics, Cambridge Univ. Press, 1992; 2001