## Combinatorics Seminar

When: Sunday January 14, 10am
Where: Schreiber 309
Speaker: Noga Alon, Tel Aviv University
Title: Cayley graphs and list-decodable zero-rate codes
## Abstract:

What is the maximum possible number of words in a binary code of length
n so that there is no Hamming ball of radius (1/4+ε)n containing
more than two words?
I will show that the answer is Θ(1/ε^{3/2}). A crucial
ingredient in the proof is a construction of a family of Cayley graphs
which is useful in tackling several additional extremal problems in
Graph Theory and Geometry.
Joint work with Bukh and Polyanskiy.