Univerza na Primorskem Fakulteta za matematiko, naravoslovje in informacijske tehnologije

Szőnyi Tamás, Eötvös Loránd University, Hungary

Title: Value sets of special polynomials and blocking sets

Abstract: For a polynomial $f\in {\rm GF}(q)[x]$, let $V(f)=\{f(x)\colon x\in{\rm GF}(q)\}$ denote the value set of $f$. Cusick and Rosendahl studied the value sets of polynomials of the form $s_a(x)=x^{a}(x+1)^{\sqrt{q}-1}$, $q$ a square, and have derived several exact results, mostly in the case when $q$ is even. Their proofs depend on the arithmetic of ${\rm GF}(q)$, while we consider the connection of the problem with blocking sets in Hall planes. Our results are also valid for $q$ odd. 

This is joint work with J. De Beule, T. H\'eger and G. Vande Voorde.

Slides from the talk.