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The fundamental question of coding theory

Nigel Boston, Professor, Department of Electrical and Computer Engineering, Professor, Department of Mathematics

Date and Time: Jul 30, 2015 ( 4:00 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building


A good code has both rate k/n and relative minimum distance d/n
large. The fundamental question of coding theory is to describe the closure
of the set of points (d/n,k/n). Goppa's conjecture says that, except for isolated
points, it's the region below the curve y=1-H(x) for x<1/2, where H is the
binary entropy function. I'll describe this and a tantalizing connection with
hyperelliptic curves that led us briefly to think we'd disproved the conjecture.
(Joint work with Jing Hao.)