Projective Geometries Over Finite Fields PDF Download
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Author: James William Peter Hirschfeld
Publisher: Oxford University Press on Demand
ISBN: 9780198502951
Category : Law
Languages : en
Pages : 555
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Book Description
I. Introduction 1. Finite fields 2. Projective spaces and algebraic varieties II. Elementary general properties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities III. The line and the plane 6. The line 7. First properties of the plane 8. Ovals 9. Arithmetic of arcs of degree two 10. Arcs in ovals 11. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes Appendix Notation References.
Author: James William Peter Hirschfeld
Publisher: Oxford University Press on Demand
ISBN: 9780198502951
Category : Law
Languages : en
Pages : 555
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Book Description
I. Introduction 1. Finite fields 2. Projective spaces and algebraic varieties II. Elementary general properties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities III. The line and the plane 6. The line 7. First properties of the plane 8. Ovals 9. Arithmetic of arcs of degree two 10. Arcs in ovals 11. Cubic curves 12. Arcs of higher degree 13. Blocking sets 14. Small planes Appendix Notation References.
Author: James Hirschfeld
Publisher: Springer
ISBN: 1447167902
Category : Mathematics
Languages : en
Pages : 422
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Book Description
This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume). This revised edition includes much updating and new material. It is a mostly self-contained study of classical varieties over a finite field, related incidence structures and particular point sets in finite n-dimensional projective spaces. General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.
Author: J. W. P. Hirschfeld
Publisher: Princeton University Press
ISBN: 1400847419
Category : Mathematics
Languages : en
Pages : 717
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Book Description
This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
Author: Albrecht Beutelspacher
Publisher: Cambridge University Press
ISBN: 9780521483643
Category : Mathematics
Languages : en
Pages : 272
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Book Description
Projective geometry is not only a jewel of mathematics, but has also many applications in modern information and communication science. This book presents the foundations of classical projective and affine geometry as well as its important applications in coding theory and cryptography. It also could serve as a first acquaintance with diagram geometry. Written in clear and contemporary language with an entertaining style and around 200 exercises, examples and hints, this book is ideally suited to be used as a textbook for study in the classroom or on its own.
Author: V. I. Arnold
Publisher: Cambridge University Press
ISBN: 1139493442
Category : Mathematics
Languages : en
Pages : 91
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Book Description
V. I. Arnold reveals some unexpected connections between such apparently unrelated theories as Galois fields, dynamical systems, ergodic theory, statistics, chaos and the geometry of projective structures on finite sets. The author blends experimental results with examples and geometrical explorations to make these findings accessible to a broad range of mathematicians, from undergraduate students to experienced researchers.
Author: Harald Niederreiter
Publisher: Princeton University Press
ISBN: 140083130X
Category : Mathematics
Languages : en
Pages : 273
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Book Description
This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books
Author: Simeon Ball
Publisher: Cambridge University Press
ISBN: 1107107997
Category : Mathematics
Languages : en
Pages : 299
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Book Description
A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.
Author: Harald Niederreiter
Publisher: World Scientific
ISBN: 981448766X
Category : Mathematics
Languages : en
Pages : 460
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Book Description
The inaugural research program of the Institute for Mathematical Sciences at the National University of Singapore took place from July to December 2001 and was devoted to coding theory and cryptology. As part of the program, tutorials for graduate students and junior researchers were given by world-renowned scholars. These tutorials covered fundamental aspects of coding theory and cryptology and were designed to prepare for original research in these areas. The present volume collects the expanded lecture notes of these tutorials. The topics range from mathematical areas such as computational number theory, exponential sums and algebraic function fields through coding-theory subjects such as extremal problems, quantum error-correcting codes and algebraic-geometry codes to cryptologic subjects such as stream ciphers, public-key infrastructures, key management, authentication schemes and distributed system security.
Author: Zhexian Wan
Publisher:
ISBN:
Category : Finite fields (Algebra).
Languages : en
Pages : 416
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Book Description
This monograph provides a survey of classical groups over finite fields. Many important results, appearing for the first time in book-form, are clearly presented. Most of them have been obtained by the author and students under his supervision.
Author: Lars Kadison
Publisher: Birkhäuser Boston
ISBN: 0817639004
Category : Mathematics
Languages : en
Pages : 228
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Book Description
The techniques and concepts of modern algebra are introduced for their natural role in the study of projectile geometry; groups appear as automorphism groups of configurations, division rings appear in the study of Desargues' theorem and the study of the independence of the seven axioms given for projectile geometry.
