Course Description

MATH 8021. Algebraic Combinatorics I

Course Code MATE 8021
Course Title Algebraic Combinatorics I
Credits 3
Hours 3 per week
Prerequisites MATH 6202, MATH 8001
Description The study of the extremal properties of algebraic structures whose symmetries are of special interest and important for applications in computer and communication sciences. The following topics are studied in depth through special reading assignments, lecture presentations, and group discussions. Linear codes. t-error correcting binary codes and finite fields. Cyclic codes. Perfect codes. Block designs. Latin squares. Pairwise balanced designs. Hadamard matrices. Difference sets. Symmetric designs. Finite geometries. Singer’s theorem. Transversal designs. Group divisible designs. Steiner triple systems. Kirkman triple systems. Strongly regular graphs. Association schemes. Distance-regular graphs. Distance transitivity.
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