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Speaker: Leah Gold, Texas A&M University

Title: Coding Theory and the Cayley-Bacharach Theorem


We will start with some basics of coding theory and the definition of an evaluation code. The question of how well such an error-correcting 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 Cayley-Bacharach 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).

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