k-Arcs and dual k-arcs

Abstract

We study the relation between k-arcs and dual k-arcs. In particular, we look at the (q+2)-arcs in PG(2, q) and in PG(q−2, q), q even. It will be shown that the problem of finding all the o-polynomials of the (q+2)-arcs in PG(2, q), q even, is equivalent with the search for all the points of PG(q−2, q), q even, which extend the normal rational curve {(1, t,…t^q−2)‖∈GF(q)⁺} to a (q+2)-arc.