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.

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FoCM 2017, based on a nodethirtythree design.