Alexander Oertel

o-Polynomials and Explicit Formula for o-Monomials

Universität Rostock, 2024

https://doi.org/10.18453/rosdok_id00004695

Abstract: Hyperovals in finite Desarguesian planes of even order q are sets of q+2 points, of which no three are collinear. By association with o-polynomials over binary finite fields, they can be studied algebraically. In this thesis o-polynomials and an equivalence relation based on the equivalence under collineations of the plane are investigated. A second topic is the connection to 2-to-1 polynomials, where explicit formulas for the known o-monomials allow the construction of 2-to-1 binomials. Finally, some generalizations to fields of odd characteristic are made as well.

master thesis   free access