Coding Theory And Algebraic Geometry
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Algebraic Geometry For Coding Theory And Cryptography
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Author : Everett W. Howe
language : en
Publisher: Springer
Release Date : 2017-11-15
Algebraic Geometry For Coding Theory And Cryptography written by Everett W. Howe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-15 with Mathematics categories.
Covering topics in algebraic geometry, coding theory, and cryptography, this volume presents interdisciplinary group research completed for the February 2016 conference at the Institute for Pure and Applied Mathematics (IPAM) in cooperation with the Association for Women in Mathematics (AWM). The conference gathered research communities across disciplines to share ideas and problems in their fields and formed small research groups made up of graduate students, postdoctoral researchers, junior faculty, and group leaders who designed and led the projects. Peer reviewed and revised, each of this volume's five papers achieves the conference’s goal of using algebraic geometry to address a problem in either coding theory or cryptography. Proposed variants of the McEliece cryptosystem based on different constructions of codes, constructions of locally recoverable codes from algebraic curves and surfaces, and algebraic approaches to the multicast network coding problem are only some of the topics covered in this volume. Researchers and graduate-level students interested in the interactions between algebraic geometry and both coding theory and cryptography will find this volume valuable.
Introduction To Coding Theory And Algebraic Geometry
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Author : J. van Lint
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Introduction To Coding Theory And Algebraic Geometry written by J. van Lint and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.
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
Using Algebraic Geometry
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Author : David A. Cox
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Using Algebraic Geometry written by David A. Cox and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gr"obner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility. The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Gr"obner bases. The book does not assume the reader is familiar with more advanced concepts such as modules.
Coding Theory And Algebraic Geometry
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Author : Henning Stichtenoth
language : en
Publisher: Springer
Release Date : 2006-11-15
Coding Theory And Algebraic Geometry written by Henning Stichtenoth and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
Coding Theory And Algebraic Geometry
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Author : Henning Stichtenoth
language : en
Publisher:
Release Date : 2014-01-15
Coding Theory And Algebraic Geometry written by Henning Stichtenoth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Elements Of Algebraic Coding Theory
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Author : Lekh R. Vermani
language : en
Publisher: Routledge
Release Date : 2022-01-26
Elements Of Algebraic Coding Theory written by Lekh R. Vermani and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-26 with Mathematics categories.
Coding theory came into existence in the late 1940s and is concerned with devising efficient encoding and decoding procedures. The book is intended as a principal text for first courses in coding and algebraic coding theory, and is aimed at advanced undergraduates and recent graduates as both a course and self-study text. BCH and cyclic, Group codes, Hamming codes, polynomial as well as many other codes are introduced in this textbook. Incorporating numerous worked examples and complete logical proofs, it is an ideal introduction to the fundamental of algebraic coding.
Algebraic Function Fields And Codes
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Author : Henning Stichtenoth
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Algebraic Function Fields And Codes written by Henning Stichtenoth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-11 with Mathematics categories.
This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.
Handbook Of Coding Theory
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Author : Vera Pless
language : en
Publisher: North Holland
Release Date : 1998-11-16
Handbook Of Coding Theory written by Vera Pless and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-16 with Computers categories.
Introduction To Coding Theory
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Author : J. H. van Lint
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Introduction To Coding Theory written by J. H. van Lint and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Coding theory is still a young subject. One can safely say that it was born in 1948. It is not surprising that it has not yet become a fixed topic in the curriculum of most universities. On the other hand, it is obvious that discrete mathematics is rapidly growing in importance. The growing need for mathe maticians and computer scientists in industry will lead to an increase in courses offered in the area of discrete mathematics. One of the most suitable and fascinating is, indeed, coding theory. So, it is not surprising that one more book on this subject now appears. However, a little more justification of the book are necessary. A few years ago it was and a little more history remarked at a meeting on coding theory that there was no book available an introductory course on coding theory (mainly which could be used for for mathematicians but also for students in engineering or computer science). The best known textbooks were either too old, too big, too technical, too much for specialists, etc. The final remark was that my Springer Lecture Notes (# 201) were slightly obsolete and out of print. Without realizing what I was getting into I announced that the statement was not true and proved this by showing several participants the book Inleiding in de Coderingstheorie, a little book based on the syllabus of a course given at the Mathematical Centre in Amsterdam in 1975 (M. C. Syllabus 31).