题目：Intersection Distribution and Its Application

报告人：(Li Shuxing), Simon Fraser University, Canada

报告时间：2020.9.26 8:30—9:30

会议地址/链接：https://meeting.tencent.com/s/3oOImSk5NwWR

会议 ID：572 282 353（无密码）

摘要：

Given a polynomial f over finite field Fq, its intersection distribution concerns the collective behaviour of a series of polynomials {f(x) + cx | c\in Fq}. Each polynomial f canonically induces a (q + 1)-set Sf in the classical projective plane PG(2; q) and the intersection distribution of f reflects how the point set Sf interacts with the lines in PG(2; q).

Motivated by the long-standing open problem of classifying oval monomials, which are monomials over F2m having the same intersection distribution as x2, we consider the next simplest case: classifying monomials over Fq having the same intersection distribution as x3. Some characterizations of such monomials are derived and consequently a conjectured complete list is proposed.

Among the conjectured list, we identify two exceptional families of monomials over F3m. Interestingly, new examples of Steiner triple systems follow from them, which are nonisomorphic to the classical ones.

This is joint work with Gohar Kyureghyan and Alexander Pott.