Penn Arts & Sciences Logo

Algebra Seminar

Monday, March 30, 2015 - 3:15pm

Nathan Kaplan

Yale University

Location

University of Pennsylvania

DRL 4N30

One of the main problems in coding theory is to find large linear subspaces of (F_q)^n so that any two elements differ in at least d coordinates. Many of the best constructions we have for this problem come from evaluating each element of a vector space of polynomials at a specified set of points. This includes the classical Reed-Solomon and Reed-Muller codes. We will discuss how interesting codes arise from families of curves in the projective plane and from degree d polynomials on P^1. We will see how these codes are related to special configurations of points in projective space and give connections to modular forms.

Stream Video URL