Rational Point Counts for del Pezzo Surfaces over Finite Fields and Coding Theory
Contributors: Elkies, Noam D.; Harris, Joe; Kumar, Abhinav
Published: 2013
Language: eng
Description: The goal of this thesis is to apply an approach due to Elkies to study the distribution of rational point counts for certain families of curves and surfaces over finite fields. A vector space of polynomials over a fixed finite field gives rise to a linear code, and the weight enumerator of this code gives information about point count distributions. The MacWilliams theorem gives a relation between the weight enumerator of a linear code and the weight enumerator of its dual code.
Notes: Keywords: Coding Theory, del Pezzo Surface, Finite Fields, Rational Points, Weight Enumerator.

Thesis Ph.D. Harvard University 2013