Maura Paterson

The Spectrum of the Non-Hitting Index of Polynomials over Finite Fields

Univariate polynomials over finite fields are used in constructing many types of combinatorial object, and have applications in coding theory and cryptography. In a 2020 paper, Li and Pott introduced the notion of the non-hitting index of a polynomial f over GF(q): it is the number of lines of the form y=mx+c that do not contain any points of the graph y=f(x). For any prime power q, the spectrum Spec(q) of the non-hitting index consists of the set of values for the non-hitting index that are attained by some univariate polynomial over GF(q).

In this talk we discuss some background context for the introduction of this definition, and survey recent results and open problems.