Finite Fields and Discrete Mathematics

Abstract

In this chapter we concentrate on new applications of finite fields which emerged quite recently. Such applications include, but are not limited to, cryptography, extremal graph theory, polynomial mappings and complexity theory which are extremely quickly developing areas posing a number exciting questions directly related to the theory of finite fields. Many classical applications of finite fields to such areas of discrete mathematics as combinatorics (in the construction of a number of combinatorial designs), finite geometries and to other areas of discrete mathematics have been described in [279, 280, 445, 1258, 1741, 1743, 1808, 2816], see also Chapters 5, 6, and 7 of this book. Here we only discuss several works, which have to do with new applications of finite fields.