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  • 1
    UID:
    b3kat_BV044432849
    Format: 1 Online-Ressource (XIV, 515 Seiten, 126 illus., 73 illus. in color)
    ISBN: 9783319569321
    Series Statement: Springer proceedings in mathematics & statistics volume 198
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-319-56930-7
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Computeralgebra ; Anwendung ; Konferenzschrift
    URL: Volltext  (URL des Erstveröffentlichers)
    Author information: Kotsireas, Ilias S. 1968-
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  • 2
    UID:
    almafu_BV044432849
    Format: 1 Online-Ressource (XIV, 515 Seiten, 126 illus., 73 illus. in color).
    ISBN: 978-3-319-56932-1
    Series Statement: Springer proceedings in mathematics & statistics volume 198
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-319-56930-7
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Computeralgebra ; Anwendung ; Konferenzschrift
    URL: Volltext  (URL des Erstveröffentlichers)
    Author information: Kotsireas, Ilias S. 1968-
    Library Location Call Number Volume/Issue/Year Availability
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  • 3
    UID:
    gbv_1690525746
    Format: 1 Online-Ressource (viii, 444 Seiten) , Illustrationen
    Edition: Singapore World Scientific Publishing Co
    ISBN: 9789814471619 , 9789812794017
    Series Statement: Series on coding theory and cryptology v. 5
    Content: 1. Algebraic geometry codes: general theory / I. M. Duursma -- 2. The decoding of algebraic geometry codes / P. Beelen and T. Hoholdt -- 3. The key equation for one-point codes / M. E. O'Sullivan and M. Bras-Amorós -- 4. Evaluation codes from an affine variety code perspective / O. Geil -- 5. Asymptotically good codes / H. Niederreiter and F. Özbudak -- 6. Algebraic curves with many points over finite fields / F. Torres -- 7. Algebraic geometry codes from higher dimensional varieties / J. B. Little -- 8. Toric codes / E. Martínez-Moro and D. Ruano -- 9. Algebraic geometric codes over rings / K. G. Bartley and J. L. Walker -- 10. Generalized hamming weights and trellis complexity / C. Munuera -- 11. Algebraic geometry constructions of convolutional codes / J. A. Domínguez Pérez, J. M. Muñoz Porras and G. Serrano Sotelo -- 12. Quantum error-correcting codes from algebraic curves / J.-L. Kim and G. L. Matthews.
    Content: Advances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of a part of the information due to either interferences in the telecommunications or degradation of the information-storing support (for instance, compact disc). An error-correcting code thus adds extra information to the message to be transmitted with the aim of recovering the sent information. With contributions from renowned researchers, this pioneering book will be of value to mathematicians, computer scientists, and engineers in information theory
    Additional Edition: ISBN 9789812794000
    Language: English
    Keywords: Electronic books
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  • 4
    UID:
    almahu_9947417184502882
    Format: 1 online resource (xiii, 240 pages : illustrations)
    Edition: Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2015
    ISBN: 9781470425661 (online)
    Series Statement: Contemporary mathematics, v. 642
    Note: Some Applications of the Fourier Transform in Algebraic Coding Theory / , A Semigroup Approach to Complete Decoding / , Gröbner Bases Methods in Coding Theory / , An Introduction to Algebraic Geometry Codes / , Evaluation Codes and Plane Valuations / , Vector Bundles with a View Toward Coding Theory / , Algebraic-Geometric Codes from Rational Surfaces / , Equivalence Classes and Structures of Constacyclic Codes Over Finite Fields / , On Repeated-Root Constacyclic Codes of Prime Power Length Over Polynomial Residue Rings / , Mode of access : World Wide Web
    Additional Edition: Print version: Algbra for secure and reliable communication modeling : ISSN 0271-4132 ISBN 9781470410186
    Language: English
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  • 5
    UID:
    almahu_BV044506005
    Format: xiv, 515 Seiten : , Illustrationen, Diagramme (teilweise farbig).
    ISBN: 978-3-319-56930-7
    Series Statement: Springer proceedings in mathematics & statistics Volume 198
    Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-3-319-56932-1
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Computeralgebra ; Anwendung ; Konferenzschrift
    Author information: Kotsireas, Ilias S. 1968-
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  • 6
    Online Resource
    Online Resource
    Hackensack, NJ :World Scientific,
    UID:
    almahu_9948317669402882
    Format: vii, 325 p.
    Edition: Electronic reproduction. Ann Arbor, MI : ProQuest, 2015. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.
    Series Statement: Series on coding theory and cryptology ; v. 8
    Language: English
    Keywords: Electronic books.
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  • 7
    UID:
    edocfu_BV044432849
    Format: 1 Online-Ressource (XIV, 515 Seiten, 126 illus., 73 illus. in color).
    ISBN: 978-3-319-56932-1
    Series Statement: Springer proceedings in mathematics & statistics volume 198
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-319-56930-7
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Computeralgebra ; Anwendung ; Konferenzschrift
    URL: Volltext  (URL des Erstveröffentlichers)
    Author information: Kotsireas, Ilias S. 1968-
    Library Location Call Number Volume/Issue/Year Availability
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  • 8
    UID:
    edoccha_BV044432849
    Format: 1 Online-Ressource (XIV, 515 Seiten, 126 illus., 73 illus. in color).
    ISBN: 978-3-319-56932-1
    Series Statement: Springer proceedings in mathematics & statistics volume 198
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-319-56930-7
    Language: English
    Subjects: Mathematics
    RVK:
    Keywords: Computeralgebra ; Anwendung ; Konferenzschrift
    URL: Volltext  (URL des Erstveröffentlichers)
    Author information: Kotsireas, Ilias S. 1968-
    Library Location Call Number Volume/Issue/Year Availability
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  • 9
    UID:
    gbv_1653996447
    Format: Online-Ressource (XIV, 515 p. 126 illus., 73 illus. in color, online resource)
    ISBN: 9783319569321
    Series Statement: Springer Proceedings in Mathematics & Statistics 198
    Content: An algebraic method to compute the mobility of closed-loop overconstrained mechanisms (Ali, Moinet, Serre) -- Simplicial topological coding and homology of spin networks (Berec) -- Trial set and Groebner bases for binary codes (Borges-Quintana, Borges-Trenard, Martiınez-Moro) -- Automated Study of Envelopes of 1-parameter Families of Surfaces (Dana-Picard, Zehavi) -- Complex Roots of Quaternion Polynomials (Dospra, Poulakis) -- Mathematical renormalization in quantum electrodynamics via noncommutative generating series (Duchamp, Ngoc Minh, Quoc Hoan, Penson, Simonnet) -- The root lattice A2 in the construction of substitution tilings and singular hypersurfaces (Escudero) -- Finding eigenvalues of self-maps with the Kronecker canonical form (Ethier, Jablonski, Mrozek) -- Algorithm for Predicting Mathematical Formulae from Linear Strings for Mathematical Inputs (Fukui) -- Algebraic Modelling of Covering Arrays (Garn, Simos) -- Applications of Signatures Curves to Characterize Melanomas and Moles (Grim, Shakiban) -- Contemporary interpretation of a historical locus problem with the use of computer algebra (Hasek, Kovacs, Zahradnik) -- Computing the Chern-Schwartz-MacPherson Class of Complete Simplical Toric Varieties (Helmer) -- The Generalized Rabinowitsch Trick (Kapur, Sun, Wang, Zhou) -- A Web-based Quantum Computer Simulator with Symbolic Extensions (Karamitrou, Tsimpouris, Mavridi, Sgarbas) -- Dixon-EDF: The Premier Method for Solution of Parametric Polynomial Systems ( Lewis) -- Visualization of Orthonormal Triads in Cylindrical and Spherical Coordinates (Lopez-Garcia, Jimenez Zamudio, Diaz V.) -- Geometric and Computational Approach to Classical and Quantum Secret Sharing (Matsumoto, Ruano) -- Computing the Dixon Resultant with the Maple Package DR (Minimair) -- Collaborative Computer Algebra (Minimair) -- States and channels in quantum mechanics without complex numbers (Miszczak) -- Double Hough transform for estimating the position of the mandibular canal in dental radiographs (Onchis-Moaca, Zappala, Gotja, Real) -- Simple and Nearly Optimal Polynomial Root- nding by Means of Root Radii Approximation (Pan) -- A Fast Schur-Euclid-type Algorithm for Quasiseparable Polynomials (Perera, Olshevsky) -- The use of CAS Piranha for the construction of motion equations of the planetary system problem (Perminov, Kuznetsov) -- Code-Based Cryptosystems Using Generalized Concatenated Codes (Puchinger, Muelich, Ishak, Bossert) -- Univariate real root isolation over a single logarithmic extension of real algebraic numbers (Strzebonski, Tsigaridas) -- On the complexity of multivariate polynomial division (van der Hoeven) -- Preserving syntactic correctness while editing mathematical formulas (van der Hoeven, Lecerf, Raux) -- About balanced application of CAS in undergraduate mathematics (Varbanova) -- Some remarks on Taylor’s polynomials visualization using Mathematica in context of function approximation (Wojas, Krupa) -- Zooming algorithms for accurate plotting of functions of two real variables (Zeitoun, Dana-Picard)
    Content: The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development
    Additional Edition: ISBN 9783319569307
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-319-56930-7
    Language: English
    Keywords: Konferenzschrift
    URL: Volltext  (lizenzpflichtig)
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  • 10
    Online Resource
    Online Resource
    Singapore ; : World Scientific,
    UID:
    almafu_9959234698402883
    Format: 1 online resource (453 p.)
    ISBN: 981-279-401-8
    Series Statement: Series on coding theory and cryptology, v. 5
    Content: Advances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of a part of the information due to either interferences in the telecommunications or degradation of the information-storing support (for instance, compact disc). An error-correcting code thus adds extra information to the message to be transmitted with the aim of recovering the sent information. With contributions from renowned rese
    Note: Description based upon print version of record. , Contents; Preface; 1. Algebraic Geometry Codes: General Theory I.M. Duursma; Contents; Introduction; 1.1 Linear codes and the a ne line; 1.1.1 Dimension and in nite families; 1.1.2 Duality and di erentials; 1.1.3 Minimum distance; 1.1.4 Error correction; 1.1.5 Linear secret sharing schemes; 1.1.6 Weight distributions and codes over extension elds; 1.2. Cyclic codes and classical Goppa codes; 1.2.1. Reed-Solomon and BCH codes; 1.2.2. Classical Goppa codes; 1.2.3. Dual BCH codes; 1.3. Reed-Muller codes; 1.4. Geometric Goppa codes; 1.4.1. Curves and linear codes , 1.4.2. Duality and differentials1.4.3. Families of curves; 1.4.4. One-point codes; 1.4.5. Two-point codes; 1.4.6. Error correction; 1.4.7. Secret reconstruction for algebraic-geometric LSSSs; 1.4.8. Weight distributions; 1.5. Bibliographic notes; References; 2. The Decoding of Algebraic Geometry Codes P. Beelen and T. H holdt; Contents; 2.1. Introduction; 2.2. The basic algorithm; 2.2.1. Decoding; 2.2.2. The basic algorithm for decoding of algebraic geome- try codes; 2.3. Syndrome formulation of the basic algorithm; 2.4. The generalized order bound; 2.5. Majority voting , 2.6. List decoding of algebraic geometry codes2.7. Syndrome formulation of list decoding; 2.8. Literature; References; 3. The Key Equation for One-Point Codes M.E. O'Sullivan and M. Bras-Amor os; Contents; 3.1. Introduction; 3.2. The key equation for Reed-Solomon codes; 3.2.1. Reed-Solomon codes; 3.2.2. Polynomials for decoding; 3.2.3. The key equation and the Berlekamp-Massey algorithm; 3.2.4. Error evaluation without the evaluator polynomial; 3.2.5. Connections to the Euclidean algorithm; 3.3. The key equation for Hermitian codes; 3.3.1. The Hermitian curve; 3.3.2. Hermitian codes , 3.3.3. Polynomials for decoding3.3.4. Another basis for Fq2(x; y); 3.3.5. The key equation; 3.3.6. Solving the key equation; 3.3.7. Error evaluation without the error evalua- tor polynomials; 3.3.8. An example; 3.4. The key equation for one-point codes; 3.4.1. Curves, function fields and differentials; 3.4.2. One-point codes and their duals; 3.4.3. The trace and a dual basis; 3.4.4. Polynomials for decoding; 3.4.5. The key equation and its solution; 3.4.6. Error evaluation without the error evaluator polynomials; 3.5. Bibliographical notes; References , 4. Evaluation Codes from an Affine Variety Code Perspective O. Geil4.1. Introduction; 4.2. Affine variety codes; 4.3. Some Grobner basis theoretical tools; 4.4. A bound on the minimum distance of C(I; L); 4.5. The Feng-Rao bound for C(I; L)?; 4.6. Using weighted degree orderings; 4.7. The order domain conditions; 4.8. Weight functions and order domains; 4.9. Codes form order domains; 4.10. One-point geometric Goppa codes; 4.11. Bibliographical Notes; References; 5. Asymptotically Good Codes H. Niederreiter and F. Ozbudak; Contents; 5.1. Introduction; 5.2. Preliminaries , 5.3. Two Constructions of Asymptotically Good Codes , English
    Additional Edition: ISBN 981-279-400-X
    Language: English
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