COURSE AIMS AND OBJECTIVES:
This course is a brief overview of design theory. Emphasis is put on connections with similar geometric, combinatorial and algebraic structures, and applications in coding theory, cryptography and statistics.
COURSE DESCRIPTION AND SYLLABUS:
1. Designs. Incidence matrices. Isomorphism and automorphism. Necessary existence conditions.
2. Basic construction methods for block designs.
3. Symmetric designs. Difference family constructions.
4. Hadamard matrices and designs.
5. Finite projective and affine planes.
6. Bruck - Ryser - Chowla theorem.
7. Collineation (automorphism) groups.
8. Error correcting codes.
9. Links between designs and linear codes.
10. Steiner triple systems and quasigroups.
11. Latin squares, orthogonality and generalizations.
12. Some applications of designs in cryptography.
13. Some applications of designs in statistics.