Infinite family of large complete arcs in PG(2, q n ), with q odd and n > 1 odd

Abstract

For q odd and n > 1 odd, a new infinite family of large complete arcs K? in PG(2, q n ) is constructed from complete arcs K in PG(2, q) which have the following property with respect to an irreducible conic $${\mathcal{C}}$$ in PG(2, q): all the points of K not in $${\mathcal{C}}$$ are all internal or all external points to $${\mathcal{C}}$$ according as q ? 1 (mod 4) or q ? 3 (mod 4).