Applications of Polynomials Over Finite Fields (original) (raw)

This work explores the applications of polynomials over finite fields in the context of combinatorially defined point sets, particularly within projective geometries. It discusses the mathematical framework, including definitions, relevant methods, and results associated with polynomials, notably the Rédei polynomial, along with their algebraic and geometric interpretations. By examining intersection numbers and the relationships between different types of point sets, the study reveals important stability results and new characterizations of classical problems in finite Galois geometry.