Toric Geometry in Coding Theory

Coding theory is concerned with detecting and correcting errors in data transmission. In 1982 Tsfasman, Vladut, and Zink discovered that codes constructed from certain families of algebraic curves have better asymptotic parameters than any previous constructions. This motivated a great activity in applying methods of algebraic geometry to coding. I will talk about a relatively new family of algebraic geometry codes called toric codes. A toric code is defined by evaluating sections of a line bundle L on a toric variety X at a finite set of points Z on X. We will see how basic parameters of a toric code depend on combinatorics of the lattice polytope associated with L and on geometry of the set of points Z.