LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	512.3
Title	Topics in Galois Fields ([EBook]) / by Dirk Hachenberger, Dieter Jungnickel.
Author	Hachenberger, Dirk
Added Personal Name	Jungnickel, Dieter
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2020.
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2020.
Physical Details	XIV, 785 p. 11 illus. : online resource.
Series	Algorithms and computation in mathematics 1431-1550 ; ; 29
ISBN	9783030608064
Summary Note	This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.:
Contents note	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.
Mode of acces to digital resource	Digital book. Cham Springer Nature 2020. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format
System details note	- Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-030-60806-4
Links to Related Works	Subject References: Algebra . Combinatorics . Computer science-Mathematics . Field Theory and Polynomials . Field theory (Physics) . Mathematics of Computing . Number Theory . Authors: author . Hachenberger, Dirk . Jungnickel, Dieter . Corporate Authors: SpringerLink (Online service) . Series: Algorithms and computation in mathematics . Classification: 512.3 .

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Topics in Galois Fields

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