A survey on galois geometries and related open problems

In this study, by examining the Galois geometry, which is a branch of finite geometry, what affine and projective planes are, on which structure they are built on and the algebraic structures required for this are explained. Examples are given on the Fano plane, which is the most basic and smallest projective plane. In addition, the incidence matrix and latin squares, which facilitate the understanding of projective planes, are mentioned. Some information has been given in the light of the studies about which order projective planes exist or not. Some basic structures are described in projective planes and projective 3-space. In the last part, as an application of projective planes, the connections between arcs and MDS or NMDS codes are emphasized. Unsolved questions, which are expressed as open problems, will be given sequentially where the related topics are.