Student Algebraic Geometry Seminar

A linear code is a subspace of $\mathbb{F}_q^n$ consisting of vectors that are pairwise distinct from each other at (hopefully) many different coordinates. One way of producing good codes comes from taking sections of line bundles on curves over finite fields. In this talk I will explain the construction, and continue on to discuss constructions and bounds regarding the number of rational points on a curve over a finite field, because, as we will see, curves with a large number of points relative to their genus produce the best codes. Speaker(s): Andy Gordon (Michigan)