A family of ovoids in PG(3, 2^m) from cyclic codes

Abstract

Ovoids in $\PG(3, q)$ have been an interesting topic in coding theory, combinatorics, and finite geometry for a long time. So far only two families are known. The first is the elliptic quadratics and the second is the Tits ovoids. In this article, we present a family of ovoids in $\PG(3, 2^m)$ for all $m$ which are from a family of irreducible cyclic codes.