Topics in Galois Fields (Innbundet)

Serie: Algorithms and Computation in Mathematics 29



Forfatter: og
Innbinding: Innbundet
Utgivelsesår: 2020
Antall sider: 785
Forlag: Springer Nature Switzerland AG
Språk: Engelsk
Serienummer: 29
ISBN/EAN: 9783030608040
Kategori: Data og Matematikk
Omtale Topics in Galois Fields
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.

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