Reed-Solomon codes are widely used in coding theory due to their good parameters and ease of decoding. Goppa codes can in a way be viewed as a generalization of Reed-Solomon codes which, for the most part, maintain these nice properties.
In this talk, I hope to briefly recall some basics of coding theory and the definition of Reed-Solomon codes. In what appears to be tangential, I will talk a little about divisors on algebraic curves. However, the definition of Goppa codes should bring everything back together. Time permitting, I will talk about what makes these codes so great.
This is a talk by Nathan Ilten of Freie Universität Berlin / Berlin Mathematical School, given at the "What is ...?" seminar at the Freie...