-
Natural sciences
- Geometry
Galois geometries concerns research of geometry over finite fields. This research area investigates many different substructures of finite projective spaces, finite classical polar spaces and other finite incidence structures. Many of these substructures are first of all investigated because of their geometrical relevance, but many of these substructures are also relevant for or arise from other mathematical areas, such as coding theory, cryptography, and graph theory. Galois geometries is in fact pure mathematics, close to practical applications. The classical example is the link between arcs in finite projective spaces and linear MDS codes in coding theory, but there are many other links, and new links keep arising. Recently, the new link between subspace codes and wireless communications arose. This shows that Galois geometries is a research area which keeps increasing in relevance.