Topics in Galois Fields (Hardcover)

Basic Algebraic Structures and Elementary Number Theory.- Basics on Polynomials- Field Extensions and the Basic Theory of Galois Fields.- The Algebraic Closure of a Galois Field.- Irreducible Polynomials over Finite Fields.- Factorization of Univariate Polynomials over Finite Fields.- Matrices over Finite Fields.- Basis Representations and Arithmetics.- Shift Register Sequences.- Characters, Gauss Sums, and the DFT.- Normal Bases and Cyclotomic Modules.- Complete Normal Bases and Generalized Cyclotomic Modules.- Primitive Normal Bases.- Primitive Elements in Affin Hyperplanes.- List of Symbols.- References.- Index.