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000944326 019__ $$a1201562162
000944326 020__ $$a9783030608064$$q(electronic book)
000944326 020__ $$a3030608069$$q(electronic book)
000944326 020__ $$z3030608042
000944326 020__ $$z9783030608040
000944326 035__ $$aSP(OCoLC)on1198559148
000944326 035__ $$aSP(OCoLC)1198559148$$z(OCoLC)1201562162
000944326 040__ $$aYDX$$beng$$cYDX$$dFIE
000944326 049__ $$aISEA
000944326 08214 $$a512.3
000944326 1001_ $$aHachenberger, Dirk.
000944326 24510 $$aTopics in galois fields.
000944326 260__ $$a[S.l.] :$$bSPRINGER,$$c2020.
000944326 300__ $$a1 online resource
000944326 336__ $$atext$$btxt$$2rdacontent
000944326 337__ $$acomputer$$bc$$2rdamedia
000944326 338__ $$aonline resource$$bcr$$2rdacarrier
000944326 4901_ $$aAlgorithms and Computation in Mathematics,$$x1431-1550 ;$$v29
000944326 5050_ $$aBasic Algebraic Structures and Elementary Number Theory -- Basics on Polynomials- Field Extensions and the Basic Theory of Galois Fields -- The Algebraic Closure of a Galois Field -- Irreducible Polynomials over Finite Fields -- Factorization of Univariate Polynomials over Finite Fields -- Matrices over Finite Fields -- Basis Representations and Arithmetics -- Shift Register Sequences -- Characters, Gauss Sums, and the DFT -- Normal Bases and Cyclotomic Modules -- Complete Normal Bases and Generalized Cyclotomic Modules -- Primitive Normal Bases -- Primitive Elements in Affin Hyperplanes -- List of Symbols -- References -- Index.
000944326 506__ $$aAccess limited to authorized users.
000944326 520__ $$aThis monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.--$$cProvided by publisher.
000944326 650_0 $$aAlgebra.
000944326 650_0 $$aField theory (Physics)
000944326 650_0 $$aNumber theory.
000944326 650_0 $$aCombinatorial analysis.
000944326 650_0 $$aComputer science$$xMathematics.
000944326 77608 $$iPrint version: $$z3030608042$$z9783030608040$$w(OCoLC)1193131608
000944326 830_0 $$aAlgorithms and computation in mathematics ;$$v29.$$x1431-1550
000944326 852__ $$bebk
000944326 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=https://dx.doi.org/10.1007/978-3-030-60806-4$$zOnline Access
000944326 909CO $$ooai:library.usi.edu:944326$$pGLOBAL_SET
000944326 980__ $$aEBOOK
000944326 980__ $$aBIB
000944326 982__ $$aEbook
000944326 983__ $$aOnline
000944326 994__ $$a92$$bISE