On the uniqueness of \((q+1)_ 4\)-arcs of \(PG(4,q),q=2^ h,h\vee\)
A \(k_ r\)-arc is a set of k points of PG(r,q), no \(r+1\) of which are linearly dependent. The authors prove that (1) in PG(3,q) with \(q=2^ h\) and \(h\geq 3\), every \(q_ 3\)-arc can be uniquely completed to a \((q+1)_ 3\)-arc; (2) in PG(4,q) with \(q=2^ h\) and \(h\geq 3\), every \((q+1)_ 4\)- arc is a normal rational curve.
scientific article; zbMATH DE number 3849978