Syllabus
Application of linear dependence and independence - cardinality of nearly-disjoint set systems, equiangular line systems, two-distance point sets.
Set systems with prescribed parity of intersections.
Eigenvalue techniques - spectra of graphs, interlacing of eigenvalues, Moore graphs.
Perfect codes in Hamming metrics and generalization to distance-regular graphs, Biggs's proof of Lloyd theorem, van Lint-Tietavainen proof of nonexistence of perfect codes over finite fields.
Seidel's switching.
Construction of Golay codes.
Annotation
Advanced course in Computer Science
Applications of linear algebraic methods in graph theory and combinatorics.
Linear dependence and independence of vectors, equiangular lines, two-distance sets, almost disjoint set systems.
Determinants.
Eigenvalues and eigenvectors, Moore graphs, strongly regular graphs.
Seidel's switching.
Error-correcting codes, namely perfect codes in Hamming metrics.
Theory of distance regular graphs and Biggs's proof of Lloyd's theorem.
Van Lint-Tietavainen's proof of nonexistence of perfect codes over finite fields.