Codes, Curves, and Configurations of Points

Nathan Kaplan (Yale)

One of the main problems in coding theory is to find large subsets of (F_q)^n such that any two elements differ in at least d coordinates. Many of the best constructions we have come from evaluating each element of a vector space of polynomials at a specified set of rational points. These include classical and projective Reed-Solomon and Reed-Muller codes. We will discuss how interesting codes arise from families of curves over finite fields and how these constructions are related to special configurations of points in projective space. We will see applications to rational point counts for del Pezzo surfaces and connections to modular forms.

Tuesday, February 24th, at 4:00pm in HBH 227

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