Large caps (Q1402876)

A cap in a projective geometry \(PG(N,q)\) or affine geometry \(AG(N,q)\) is a set of points no three of which are collinear. It is well known that the theory of caps in projective spaces over finite fields is identical to the theory of linear codes of minimum distance 4. An important problem is to determine the maximum size \(m_2(N,q)=m_2(PG(N,q))\) (\(m_2(AG(N,q))\), respectively) of a cap in \(PG(N,q)\) (\(AG(N,q)\), respectively). The author surveys known and new results on this problem, as well as on a wide variety of related problems.