Arc in a finite plane

Summary

A $k$-arc in a finite projective plane is a set of $k$ points with no three on a common line. In a plane of order $n$ a $k$-arc has at most $n + 2$ points, and at most $n + 1$ points when $n$ is odd. Arcs of maximal size, such as conics, are central objects of finite geometry and are linked to maximum distance separable codes.