© Universität Augsburg

Dirk Hachenberger, Dieter Jungnickel


Topics in Galois Fields

Series: Algorithms and Computation in Mathematics


Springer Verlag, 2020

ISBN 978-3-030-60806-4

1st ed. 2020, XIV, 785 p. 11 illus.

  • 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.
© Universität Augsburg

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.


Ein außergewöhnlicher Blick ins Buch