Error-Correcting Codes and Points over Finite Fields

Professor: Nathan Kaplan

Description: In this project, we will investigate classes of codes using tools from algebra, number theory, and geometry. There are many interesting codes that have constructions that come from algebra, for example, we will consider codes that come from evaluating polynomials. We will consider connections between classes of codes and the geometry of special collections of points in vector spaces over finite fields.

Preferred Qualifications: Students should be comfortable with linear algebra. Familiarity with abstract algebra and/or number theory is a plus, but is not necessary. I hope that we will generate a lot of data using a computer algebra system. It is not important that every student already be familiar with mathematical programming, but I am hoping to recruit at least one student for my research group who is enthusiastic about writing programs.