Dirk Hachenberger

(Author)

Topics in Galois Fields (2020)Hardcover - 2020, 30 September 2020

Topics in Galois Fields (2020)
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Part of Series
Algorithms and Computation in Mathematics
Print Length
785 pages
Language
English
Publisher
Springer
Date Published
30 Sep 2020
ISBN-10
3030608042
ISBN-13
9783030608040

Description

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.

Product Details

Authors:
Dirk HachenbergerDieter Jungnickel
Book Edition:
2020
Book Format:
Hardcover
Country of Origin:
NL
Date Published:
30 September 2020
Dimensions:
23.39 x 15.6 x 4.29 cm
ISBN-10:
3030608042
ISBN-13:
9783030608040
Language:
English
Location:
Cham
Pages:
785
Publisher:
Weight:
1288.2 gm

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