Applications Of Algebraic Geometry To Coding Theory Physics And Computation

Author : Ciro Ciliberto,Friedrich Hirzebruch,Rick Miranda,Mina Teicher
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401010115

Get Book

Applications of Algebraic Geometry to Coding Theory, Physics and Computation by Ciro Ciliberto,Friedrich Hirzebruch,Rick Miranda,Mina Teicher Pdf

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.

Author : Edgar Martinez-Moro,Edgar Martínez-Moro
Publisher : World Scientific
Page : 334 pages
File Size : 55,6 Mb
Release : 2013
Category : Computers
ISBN : 9789814335751

Get Book

Algebraic Geometry Modeling in Information Theory by Edgar Martinez-Moro,Edgar Martínez-Moro Pdf

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.

Author : Harald Niederreiter,Chaoping Xing
Publisher : Princeton University Press
Page : 272 pages
File Size : 44,7 Mb
Release : 2009-09-21
Category : Mathematics
ISBN : 9781400831302

Get Book

Algebraic Geometry in Coding Theory and Cryptography by Harald Niederreiter,Chaoping Xing Pdf

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 : Michael Tsfasman,Serge Vlǎduţ,Dmitry Nogin
Publisher : American Mathematical Soc.
Page : 453 pages
File Size : 48,8 Mb
Release : 2019-07-02
Category : Coding theory
ISBN : 9781470448653

Get Book

Algebraic Geometry Codes: Advanced Chapters by Michael Tsfasman,Serge Vlǎduţ,Dmitry Nogin Pdf

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.

Author : J. van Lint,G. van der Geer
Publisher : Birkhäuser
Page : 82 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034892865

Get Book

Introduction to Coding Theory and Algebraic Geometry by J. van Lint,G. van der Geer Pdf

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

Author : David A. Cox Dinesh N. Manocha Bernd Sturmfels
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 42,7 Mb
Release : 2024-07-03
Category : Geometry, Algebraic
ISBN : 082186758X

Get Book

Applications of Computational Algebraic Geometry by David A. Cox Dinesh N. Manocha Bernd Sturmfels Pdf

Author : Henning Stichtenoth,Michael A. Tsfasman
Publisher : Springer
Page : 235 pages
File Size : 41,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540472674

Get Book

Coding Theory and Algebraic Geometry by Henning Stichtenoth,Michael A. Tsfasman Pdf

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.

Author : David Evans
Publisher : American Mathematical Soc.
Page : 166 pages
File Size : 53,5 Mb
Release : 2005
Category : Computers
ISBN : 9780821836002

Get Book

Coding Theory and Quantum Computing by David Evans Pdf

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.

Author : Tzuong-tsieng Moh
Publisher : World Scientific
Page : 266 pages
File Size : 43,8 Mb
Release : 2022-02-18
Category : Mathematics
ISBN : 9789811220982

Get Book

Introduction To Algebraic Coding Theory by Tzuong-tsieng Moh Pdf

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.

Author : Edgar Martinez-Moro
Publisher : World Scientific
Page : 453 pages
File Size : 41,6 Mb
Release : 2008
Category : Computers
ISBN : 9789812794017

Get Book

Advances in Algebraic Geometry Codes by Edgar Martinez-Moro Pdf

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.

Author : David A. Cox,Dinesh N. Manocha
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 51,5 Mb
Release : 1998
Category : Geometry, Algebraic
ISBN : 9780821807507

Get Book

Applications of Computational Algebraic Geometry by David A. Cox,Dinesh N. Manocha Pdf

This book introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Gröbner 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 profound impact in recent years. At the same time, the mathematics used in computational algebraic geometry is unusually elegant and accessible, which makes the subject easy to learn and easy to apply. This book begins with an introduction to Gröbner 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.

Author : N.E. Hurt
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 42,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9789401702515

Get Book

Many Rational Points by N.E. Hurt Pdf

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

Author : Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning
Publisher : Springer Science & Business Media
Page : 656 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642558269

Get Book

Computer Algebra Handbook by Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning Pdf

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.

Author : Leo Dorst,Chris Doran,Joan Lasenby
Publisher : Springer Science & Business Media
Page : 479 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200895

Get Book

Applications of Geometric Algebra in Computer Science and Engineering by Leo Dorst,Chris Doran,Joan Lasenby Pdf

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.

Author : Ilias S. Kotsireas,Edgar Martínez-Moro
Publisher : Springer
Page : 515 pages
File Size : 54,6 Mb
Release : 2017-07-26
Category : Mathematics
ISBN : 9783319569321

Get Book

Applications of Computer Algebra by Ilias S. Kotsireas,Edgar Martínez-Moro Pdf

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.