Arcs in PG(n,q), MDS-codes and three fundamental problems of B. Segre - some extensions (Q921584)

An s-arc of points in an n-dimensional projective space over GF(q), \(s\geq n+1\), is a set of s points no \(n+1\) of which lie in a hyperplane. Of particular interest are s-arcs with maximal s. The author uses algebraic hypersurfaces associated with s-arcs in order to prove new results on questions raised by B. Segre in 1955. The questions have meanwhile attracted new interest because of their applications to MDS-codes.