Sharp groups, two-weight codes and maximal arcs

Abstract

Many rank 2 sharp groups have a normal elementary abelian subgroup whose action can be constructed from a two-weight linear code. The sharp groups of this kind are characterized using a correspondence between these two-weight codes and maximal arcs in a projective geometry. A description of those rank 2 sharp groups which occur as subgroups of an affine linear group is also given. These sharp groups are either geometric or have a normal elementary abelian subgroup corresponding to a two-weight linear code which in turn corresponds to the complement of a hyperplane in a projective geometry.