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.