1.

Record Nr.

UNISA996418203603316

Autore

Hachenberger Dirk

Titolo

Topics in Galois fields / / Dirk Hachenberger and Dieter Jungnickel

Pubbl/distr/stampa

Cham, Switzerland : , : Springer, , [2020]

©2020

ISBN

3-030-60806-9

Edizione

[1st ed. 2020.]

Descrizione fisica

1 online resource (XIV, 785 p. 11 illus.)

Collana

Algorithms and Computation in Mathematics, , 1431-1550 ; ; 29

Disciplina

512.3

Soggetti

Finite fields (Algebra)

Galois theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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.

2.

Record Nr.

UNIORUON00233059

Autore

Caroti, Stefano

Titolo

L' astrologia in Italia : profezie, oroscopi e segreti celesti, dagli zodiaci romani alla tradizione islamica, dalle corti rinascimentali alle scuole moderne : storia documenti personaggi / Stefano Caroti

Pubbl/distr/stampa

Roma, : Newton Compton editori, 1983

Descrizione fisica

308 p. : ill. ; 22 cm.

Disciplina

133.5

Soggetti

ASTROLOGIA - Italia - Storia

Lingua di pubblicazione

Italiano

Formato

Materiale a stampa

Livello bibliografico

Monografia