Download or read book Applications of Algebraic Geometry to Coding Theory Physics and Computation written by Ciro Ciliberto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory, communication networks, and computer vision. Contributions on more fundamental aspects of algebraic geometry include expositions related to counting points on varieties over finite fields, Mori theory, linear systems, Abelian varieties, vector bundles on singular curves, degenerations of surfaces, and mirror symmetry of Calabi-Yau manifolds.
Download or read book Algebraic Geometry in Coding Theory and Cryptography written by Harald Niederreiter and published by Princeton University Press. This book was released on 2009-09-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Algebraic Geometry Modeling in Information Theory written by Edgar Martinez-Moro and published by World Scientific. This book was released on 2013 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.
Download or read book Algebraic Geometry Codes Advanced Chapters written by Michael Tsfasman and published by American Mathematical Soc.. This book was released on 2019-07-02 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to local_libraryBook Catalogseveral domains of mathematics. On one hand, it involves such classical areas as algebraic geometry and number theory; on the other, it is connected to information transmission theory, combinatorics, finite geometries, dense packings, and so on. The book gives a unique perspective on the subject. Whereas most books on coding theory start with elementary concepts and then develop them in the framework of coding theory itself within, this book systematically presents meaningful and important connections of coding theory with algebraic geometry and number theory. Among many topics treated in the book, the following should be mentioned: curves with many points over finite fields, class field theory, asymptotic theory of global fields, decoding, sphere packing, codes from multi-dimensional varieties, and applications of algebraic geometry codes. The book is the natural continuation of Algebraic Geometric Codes: Basic Notions by the same authors. The concise exposition of the first volume is included as an appendix.
Download or read book Introduction to Coding Theory and Algebraic Geometry written by J. van Lint and published by Birkhäuser. This book was released on 2012-12-06 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI -- CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course
Download or read book Introduction To Algebraic Coding Theory written by Tzuong-tsieng Moh and published by World Scientific. This book was released on 2022-02-18 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this age of technology where messages are transmitted in sequences of 0's and 1's through space, errors can occur due to noisy channels. Thus, self-correcting code is vital to eradicate these errors when the number of errors is small. It is widely used in industry for a variety of applications including e-mail, telephone, and remote sensing (for example, photographs of Mars).An expert in algebra and algebraic geometry, Tzuong-Tsieng Moh covers many essential aspects of algebraic coding theory in this book, such as elementary algebraic coding theories, the mathematical theory of vector spaces and linear algebras behind them, various rings and associated coding theories, a fast decoding method, useful parts of algebraic geometry and geometric coding theories.This book is accessible to advanced undergraduate students, graduate students, coding theorists and algebraic geometers.
Download or read book Computer Algebra Handbook written by Johannes Grabmeier and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.
Download or read book Applications of Computational Algebraic Geometry written by David A. Cox Dinesh N. Manocha Bernd Sturmfels and published by American Mathematical Soc.. This book was released on with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Coding Theory and Quantum Computing written by David Evans and published by American Mathematical Soc.. This book was released on 2005 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: A conference, Coding Theory and Quantum Computing, was held in Charlottesville, VA, to provide an opportunity for computer scientists, mathematicians, and physicists to interact about subjects of common interest. This proceedings volume grew out of that meeting. It is divided into two parts: "Coding Theory" and "Quantum Computing". In the first part, Harold Ward gives an introduction to coding theory. Other papers survey recent important work, such as coding theory applications of Grobner bases, methods of computing parameters of codes corresponding to algebraic curves, and problems in the theory of designs. The second part of the book covers a wide variety of directions in quantum information with an emphasis on understanding entanglement. The material presented is suitable for graduate students and researchers interested in coding theory and in quantum computing.
Download or read book Advances in Algebraic Geometry Codes written by Edgar Martinez-Moro and published by World Scientific. This book was released on 2008 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Coding Theory and Algebraic Geometry written by Henning Stichtenoth and published by Springer. This book was released on 2006-11-15 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: About ten years ago, V.D. Goppa found a surprising connection between the theory of algebraic curves over a finite field and error-correcting codes. The aim of the meeting "Algebraic Geometry and Coding Theory" was to give a survey on the present state of research in this field and related topics. The proceedings contain research papers on several aspects of the theory, among them: Codes constructed from special curves and from higher-dimensional varieties, Decoding of algebraic geometric codes, Trace codes, Exponen- tial sums, Fast multiplication in finite fields, Asymptotic number of points on algebraic curves, Sphere packings.
Download or read book Many Rational Points written by N.E. Hurt and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a source book of examples with relationships to advanced topics regarding Sato-Tate conjectures, Eichler-Selberg trace formula, Katz-Sarnak conjectures and Hecke operators." "The book will be of use to mathematicians, physicists and engineers interested in the mathematical methods of algebraic geometry as they apply to coding theory and cryptography."--Jacket
Download or read book Applications of Computational Algebraic Geometry written by Dinesh Manocha and published by American Mathematical Society(RI). This book was released on 2014-05-10 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Gr obner bases and fueled by the advent of modern computers and the rediscovery of resultants, computational algebraic geometry has grown rapidly in importance. The fact that crunching equations is now as easy as crunching numbers has had a impact in recent years. At the same time, the mathematics used in computational algebraic geometry is unusual and accessible, which makes the subject easy to learn and easy to apply. This book begins with an introduction to Gr obner bases and resultants, then discusses some of the more recent methods for solving systems of polynomial equations. A sampler of possible applications follows, including computer-aided geometric design, complex information systems, integer programming, and algebraic coding theory. The lectures in this book assume no previous acquaintance with the material.
Download or read book Algebraic Geometric Codes Basic Notions written by Michael Tsfasman and published by American Mathematical Society. This book was released on 2022-04-15 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics. On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc. The authors give a unique perspective on the subject. Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory. There are no prerequisites other than a standard algebra graduate course. The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes.
Download or read book Computing in Algebraic Geometry written by Wolfram Decker and published by Springer Science & Business Media. This book was released on 2006-05-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.
Download or read book Applications of Geometric Algebra in Computer Science and Engineering written by Leo Dorst and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.
Download or read book Applications of Computer Algebra written by Ilias S. Kotsireas and published by Springer. This book was released on 2017-07-26 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
