01030cam0 22003013 450 SON000764020210415143444.0887983742720031110d1994 |||||ita|0103 baitaIT<<Le >>due tigriEmilio SalgariA cura di Sergio Campailla, edizione integraleRomaNewton Compton Editori1994288p.ill.21 cmBiblioteca Economica NewtonSezione Ragazzi13001LAEC000192662001 *Biblioteca Economica Newton. Sezione Ragazzi13Salgari, EmilioAF00007444070174819CAMPAILLA, SergioAF00016077070ITUNISOB20210415RICAUNISOBUNISOB85383355SON0007640M 102 Monografia moderna SBNM853000797SI83355ACQUISTOSpinosaUNISOBUNISOB20200227094325.020200227094333.0SpinosaDue tigri1672453UNISOB04016nam 22007575 450 991048366510332120250424094701.03-030-60806-910.1007/978-3-030-60806-4(CKB)5590000000002295(MiAaPQ)EBC6361021(DE-He213)978-3-030-60806-4(MiAaPQ)EBC6647501(Au-PeEL)EBL6361021(OCoLC)1198559148(Au-PeEL)EBL6647501(PPN)250220962(EXLCZ)99559000000000229520200929d2020 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierTopics in Galois Fields /by Dirk Hachenberger, Dieter Jungnickel1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (XIV, 785 p. 11 illus.) Algorithms and Computation in Mathematics,2512-3254 ;293-030-60804-2 Includes bibliographical references and index.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.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 ininformation and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.Algorithms and Computation in Mathematics,2512-3254 ;29Algebraic fieldsPolynomialsAlgebraNumber theoryDiscrete mathematicsComputer scienceMathematicsField Theory and PolynomialsAlgebraNumber TheoryDiscrete MathematicsMathematics of ComputingAlgebraic fields.Polynomials.Algebra.Number theory.Discrete mathematics.Computer scienceMathematics.Field Theory and Polynomials.Algebra.Number Theory.Discrete Mathematics.Mathematics of Computing.512.3Hachenberger Dirk845494Jungnickel D.1952-MiAaPQMiAaPQMiAaPQBOOK9910483665103321Topics in Galois Fields1887565UNINA