#### Conference abstracts

Session A3 - Computational Number Theory

July 12, 18:20 ~ 19:00 - Room B6

## Rational point count distributions for plane quartic curves over finite fields

### Nathan Kaplan

### University of California, Irvine, USA - nckaplan@math.uci.edu

We use ideas from coding theory, specifically the MacWilliams theorem, to study rational point count distributions for quartic curves in the projective plane over a finite field. We explain how the set of all homogeneous quartic polynomials in three variables gives rise to an evaluation code, and how low-weight coefficients of the weight enumerator of the dual code give information about rational point count distributions for quartic curves. No previous familiarity with coding theory will be assumed.