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, maintains 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 tagential, I will talk a little about divisors in 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.