LEADER 03390nam 2200553 450 001 996418203603316 005 20220321133839.0 010 $a3-030-60806-9 024 7 $a10.1007/978-3-030-60806-4 035 $a(CKB)5590000000002295 035 $a(MiAaPQ)EBC6361021 035 $a(DE-He213)978-3-030-60806-4 035 $a(MiAaPQ)EBC6647501 035 $a(Au-PeEL)EBL6361021 035 $a(OCoLC)1198559148 035 $a(Au-PeEL)EBL6647501 035 $a(PPN)250220962 035 $a(EXLCZ)995590000000002295 100 $a20220321d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTopics in Galois fields /$fDirk Hachenberger and Dieter Jungnickel 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (XIV, 785 p. 11 illus.) 225 1 $aAlgorithms and Computation in Mathematics,$x1431-1550 ;$v29 311 $a3-030-60804-2 320 $aIncludes bibliographical references and index. 327 $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. 330 $aThis monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science. 410 0$aAlgorithms and Computation in Mathematics,$x1431-1550 ;$v29 606 $aFinite fields (Algebra) 606 $aGalois theory 615 0$aFinite fields (Algebra) 615 0$aGalois theory. 676 $a512.3 700 $aHachenberger$b Dirk$0845494 702 $aJungnickel$b D.$f1952- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418203603316 996 $aTopics in Galois Fields$91887565 997 $aUNISA LEADER 01292nam2 2200337 i 450 001 VAN0004989 005 20150211113927.346 010 $a88-02-05347-2 020 $aIT$b99 3995 100 $a20020805d1998 |0itac50 ba 101 $aita 102 $aIT 105 $a|||| ||||| 200 1 $aˆ1: Le ‰fonti scritte$fAlessandro Pizzorusso, Silvia Ferreri$gcon collaborazioni di Antonio Gambaro e Rodolfo Sacco 210 $aTorino$cUTET$d[1998] 215 $aX, 482 p.$d25 cm. 461 1$1001VAN0004987$12001 $aˆLe ‰fonti del diritto italiano.$v1 606 $aDiritto$xItalia$xFonti$3VANC003070$2FI 620 $dTorino$3VANL000001 676 $a349.45$cDiritto. Italia$v21 700 1$aPizzorusso$bAlessandro$3VANV000065$0140444 701 1$aFerreri$bSilvia$3VANV001936$0247703 702 1$aGambaro$bAntonio$3VANV002805 702 1$aSacco$bRodolfo$3VANV000658 712 $aUTET $3VANV107949$4650 801 $aIT$bSOL$c20240614$gRICA 899 $aBIBLIOTECA DEL DIPARTIMENTO DI GIURISPRUDENZA$1IT-CE0105$2VAN00 912 $aVAN0004989 950 $aBIBLIOTECA DEL DIPARTIMENTO DI GIURISPRUDENZA$d00CONS XV.D.6(1/1) $e00 13580 20020806 996 $aFonti scritte$9968487 997 $aUNICAMPANIA