Speaker:
Leah Gold, Texas A&M University
Title:
Coding Theory and the CayleyBacharach Theorem
Abstract:
We will start with some basics of coding theory and the definition of an
evaluation code. The question of how well such an errorcorrecting code
performs when it comes to detecting and correcting errors is measured by
the minimal distance of the code. For a particular type of evaluation code
J. Hansen used cohomological methods to determine a lower bound for the
minimal distance. We will explore a classical theorem of algebraic
geometry known as the CayleyBacharach Theorem, and see how a modern
version of this theorem may be used both to shorten and generalize
Hansen's proof. The talk with include an overview of the necessary
algebraic geometry. This result is joint work with John Little (College of
the Holy Cross) and Hal Schenck (Texas A&M University).
