Galois geometry

Galois geometry (so named after the 19th-century French mathematician Évariste Galois) is the branch of finite geometry that is concerned with algebraic and analytic geometry over a finite field (or Galois field).^[1] More narrowly, a Galois geometry may be defined as a projective space over a finite field.^[2]

Objects of study include affine and projective spaces over finite fields and various structures that are contained in them. In particular, arcs, ovals, hyperovals, unitals, blocking sets, ovoids, caps, spreads and all finite analogues of structures found in non-finite geometries. Vector spaces defined over finite fields play a significant role, especially in construction methods.