On $m$-ovoids of Symplectic Polar Spaces

TL;DR

This paper introduces a novel construction method for $m$-ovoids in symplectic polar spaces using strongly regular Cayley graphs, resulting in many new $m$-ovoids beyond existing field reduction techniques.

Contribution

The paper presents a new approach to construct $m$-ovoids in symplectic polar spaces from strongly regular Cayley graphs, expanding the known classes of $m$-ovoids.

Findings

Many new $m$-ovoids constructed

Method produces $m$-ovoids not obtainable by field reduction

Advances understanding of symplectic polar space structures

Abstract

In this paper, we develop a new method for constructing $m$-ovoids in the symplectic polar space $\W(2r-1,\q)$ from some strongly regular Cayley graphs in \cite{Brouwer1999Journal}. Using this method, we obtain many new $m$-ovoids which can not be derived by field reduction.