Topics in Galois Fields
By: authored by Dirk Hachenberger & Dieter Jungnickel
Edition: First edition
Series: Algorithms and Computation in Mathematics, Vol - 29
Publisher: Springer
Published: September 30, 2020
Place of publication: Cham, Switzerland
Language: eng
Format: Hardcover
Number of pages: 800
ISBN-13: 9783030608040
Copyright date: ©2020
Description: The authors give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, they emphasize the interplay between arithmetical and structural results, and the authors also introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm.
Notes: Includes modern material that has not appeared in book form before.  Develops the theory from the basics and includes a thorough discussion of infinite algebraic extensions of. Galois fields and generators thereof. 
Emphasizes (the concrete construction of) particular generators for Galois field extensions, which are motivated by several applications​. 

Contains reference (at page 761) and index (at page 777)
Table of contents: title: - Basic Algebraic Structures and Elementary Number Theory.; title: - Basics on Polynomials; title: - Field Extensions and the Basic Theory of Galois Fields.; title: - The Algebraic Closure of a Galois Field.; title: - Irreducible Polynomials over Finite Fields.; title: - Factorization of Univariate Polynomials over Finite Fields.; title: - Matrices over Finite Fields.; title: - Basis Representations and Arithmetics.; title: - Shift Register Sequences.; title: - Characters, Gauss Sums, and the DFT.; title: - Normal Bases and Cyclotomic Modules.; title: - Complete Normal Bases and Generalized Cyclotomic Modules.; title: - Primitive Normal Bases.; title: - Primitive Elements in Affin Hyperplanes.; title: - List of Symbols.; title: - References.; title: - Index.