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Table of Contents
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.
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.