Session A3 - Computational Number Theory
July 12, 18:20 ~ 19:00 - Room B6
Rational point count distributions for plane quartic curves over finite fields
University of California, Irvine, USA - firstname.lastname@example.org
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.