Arithmetic Geometry And Coding Theory

Author by : Yves Aubry
Languange : en
Publisher by : SMF
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Description : In May 2003, two events were held in the CIRM (Marseille-Luminy) devoted to arithmetic, geometry and their applications in coding theory and cryptography: a European school ``Algebraic Geometry and Information Theory'' and the 9th international conference ``Arithmetic, Geometry and Coding Theory''. Some of the courses of the conferences are published in this volume. Topics covered include: Abelian varieties, function fields and curves over finite fields, Galois group of pro-$p$-extensions, Dedekind zeta functions of number fields, numerical semigroups, Waring numbers, bilinear complexity of the multiplication in finite fields and class number problems.


Arithmetic Geometry And Coding Theory

Author by : R. Pellikaan
Languange : en
Publisher by : Walter de Gruyter
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Description : The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.


Algorithmic Arithmetic Geometry And Coding Theory

Author by : Stéphane Ballet
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the 14th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held June 3-7, 2013, at CIRM, Marseille, France. These international conferences, held every two years, have been a major event in the area of algorithmic and applied arithmetic geometry for more than 20 years. This volume contains 13 original research articles covering geometric error correcting codes, and algorithmic and explicit arithmetic geometry of curves and higher dimensional varieties. Tools used in these articles include classical algebraic geometry of curves, varieties and Jacobians, Suslin homology, Monsky-Washnitzer cohomology, and -functions of modular forms.


Arithmetic Geometry Cryptography And Coding Theory 2009

Author by : David R. Kohel
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the 12th conference on Arithmetic, Geometry, cryptography and coding Theory, held in Marseille, France from March 30 to April 3, 2009, as well as the first Geocrypt conference, held in pointe-a-pitre, guadeloupe, from April 27 to may 1, 2009, and the European science Foundation exploratory workshop on curves, coding Theory, and Cryptography, held in Marseille, France from March 25 to 29, 2009. The articles Contained in this volume come from three related symposia organized by the group Arithmetique et Theorie de I' Information in Marseille. The topics cover arithmetic properties of curves and higher dimensional varieties with applications to codes and cryptography.


Arithmetic Geometry Cryptography And Coding Theory

Author by : Stéphane Ballet
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the 17th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory (AGC2T-17), held from June 10–14, 2019, at the Centre International de Rencontres Mathématiques in Marseille, France. The conference was dedicated to the memory of Gilles Lachaud, one of the founding fathers of the AGC2T series. Since the first meeting in 1987 the biennial AGC2T meetings have brought together the leading experts on arithmetic and algebraic geometry, and the connections to coding theory, cryptography, and algorithmic complexity. This volume highlights important new developments in the field.


Arithmetic Geometry Cryptography And Coding Theory

Author by : Gilles Lachaud
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the 11th conference on $\mathrm{AGC^{2}T}$, held in Marseille, France in November 2007. There are 12 original research articles covering asymptotic properties of global fields, arithmetic properties of curves and higher dimensional varieties, and applications to codes and cryptography. This volume also contains a survey article on applications of finite fields by J.-P. Serre. $\mathrm{AGC^{2}T}$ conferences take place in Marseille, France every 2 years. These international conferences have been a major event in the area of applied arithmetic geometry for more than 20 years.


Arithmetic Geometry Cryptography And Coding Theory

Author by : Yves Aubry
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the 13th $\mathrm{AGC^2T}$ conference, held March 14-18, 2011, in Marseille, France, together with the proceedings of the 2011 Geocrypt conference, held June 19-24, 2011, in Bastia, France. The original research articles contained in this volume cover various topics ranging from algebraic number theory to Diophantine geometry, curves and abelian varieties over finite fields and applications to codes, boolean functions or cryptography. The international conference $\mathrm{AGC^2T}$, which is held every two years in Marseille, France, has been a major event in the area of applied arithmetic geometry for more than 25 years.


Arithmetic Geometry Cryptography And Coding Theory

Author by : Alp Bassa
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume contains the proceedings of the 15th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held at the Centre International de Rencontres Mathématiques in Marseille, France, from May 18–22, 2015. Since the first meeting almost 30 years ago, the biennial AGCT meetings have been one of the main events bringing together researchers interested in explicit aspects of arithmetic geometry and applications to coding theory and cryptography. This volume contains original research articles reflecting recent developments in the field.


Arithmetic Geometry Computation And Applications

Author by : Yves Aubry
Languange : en
Publisher by : American Mathematical Soc.
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Total Read : 51
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Description : For thirty years, the biennial international conference AGC T (Arithmetic, Geometry, Cryptography, and Coding Theory) has brought researchers to Marseille to build connections between arithmetic geometry and its applications, originally highlighting coding theory but more recently including cryptography and other areas as well. This volume contains the proceedings of the 16th international conference, held from June 19–23, 2017. The papers are original research articles covering a large range of topics, including weight enumerators for codes, function field analogs of the Brauer–Siegel theorem, the computation of cohomological invariants of curves, the trace distributions of algebraic groups, and applications of the computation of zeta functions of curves. Despite the varied topics, the papers share a common thread: the beautiful interplay between abstract theory and explicit results.


Codes And Curves

Author by : Judy L. Walker
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book is based on a series of lectures the author gave as part of the IAS/Park City Mathematics Institute (Utah) program on arithmetic algebraic geometry. It introduces the reader to the exciting field of algebraic geometric coding theory. Presenting the material in the same conversational tone of the lectures, the author covers linear codes, including cyclic codes, and both bounds and asymptotic bounds on the parameters of codes. Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors. This book is published in cooperation with IAS/Park City Mathematics Institute.


Arithmetic Geometry

Author by : Yves Aubry
Languange : en
Publisher by : Unknown
Format Available : PDF, ePub, Mobi
Total Read : 71
Total Download : 309
File Size : 41,9 Mb
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Description : For thirty years, the biennial international conference AGC^2T (Arithmetic, Geometry, Cryptography, and Coding Theory) has brought researchers to Marseille to build connections between arithmetic geometry and its applications, originally highlighting coding theory but more recently including cryptography and other areas as well. This volume contains the proceedings of the 16th international conference, held from June 19-23, 2017. The papers are original research articles covering a large range of topics, including weight enumerators for codes, function field analogs of the Brauer-Siegel theore.


Arithmetic Geometry Cryptography And Coding Theory

Author by : Alp Bassa
Languange : en
Publisher by : Unknown
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Total Read : 77
Total Download : 780
File Size : 53,9 Mb
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Description : This volume contains the proceedings of the 15th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held at the Centre International de Rencontres Mathématiques in Marseille, France, from May 18-22, 2015. Since the first meeting almost 30 years ago, the biennial AGCT meetings have been one of the main events bringing together researchers interested in explicit aspects of arithmetic geometry and applications to coding theory and cryptography. This volume contains original research articles reflecting recent developments in the field


Integrable Systems And Algebraic Geometry

Author by : Ron Donagi
Languange : en
Publisher by : Cambridge University Press
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Description : Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. The articles in this second volume discuss areas related to algebraic geometry, emphasizing the connections of this central subject to integrable systems, arithmetic geometry, Riemann surfaces, coding theory and lattice theory.


Arithmetic Geometry And Coding Theory Agct 2003

Author by : Jean-Paul Brasselet
Languange : en
Publisher by : SMF
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Description : The second Franco-Japanese Singularity Conference was held in the CIRM (Marseille-Luminy) in September 2002. The proceedings of the meeting published in this volume show not only the diversity, but also the consistency of the fields discussed. The main topics covered by the lectures were characteristic classes, residues, stratifications, singularities of curves and surfaces, valuations, resolution of singularities, and toric varieties. Several papers present the results recently obtained in the field so as to be accessible to non-specialists and to users of singularity theory. The volume is suitable for graduate students and research mathematicians interested in geometry and topology.


Algebraic Geometry In Coding Theory And Cryptography

Author by : Harald Niederreiter
Languange : en
Publisher by : Princeton University Press
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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


Algebraic Geometry For Coding Theory And Cryptography

Author by : Everett W. Howe
Languange : en
Publisher by : Springer
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Description : 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.


Recent Developments In The Inverse Galois Problem

Author by : Michael D. Fried
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book contains the refereed proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Recent Developments in the Inverse Galois Problem, held in July 1993 at the University of Washington, Seattle. A new review of Serre's Topics in Galois Theory serves as a starting point. The book describes the latest research on explicit presentation of the absolute Galois group of the rationals. Containing the first appearance of generalizations of modular curves, the book presents applications that demonstrate the full scope of the Inverse Galois Problem. In particular, the papers collected here show the ubiquity of the applications of the Inverse Galois Problem and its compelling significance. The book will serve as a guide to progress on the Inverse Galois Problem and as an aid in using this work in other areas of mathematics. This includes coding theory and other finite field applications. Group theory and a first course in algebraic curves are sufficient for understanding many papers in the volume. Graduate students will find this an excellent reference to current research, as it contains a list of problems appropriate for thesis material in arithmetic geometry, algebraic number theory, and group theory.


Topics In Geometry Coding Theory And Cryptography

Author by : Arnaldo Garcia
Languange : en
Publisher by : Springer Science & Business Media
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Description : The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.


Directions In Number Theory

Author by : Ellen E. Eischen
Languange : en
Publisher by : Springer
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Description : Exploring the interplay between deep theory and intricate computation, this volume is a compilation of research and survey papers in number theory, written by members of the Women In Numbers (WIN) network, principally by the collaborative research groups formed at Women In Numbers 3, a conference at the Banff International Research Station in Banff, Alberta, on April 21-25, 2014. The papers span a wide range of research areas: arithmetic geometry; analytic number theory; algebraic number theory; and applications to coding and cryptography. The WIN conference series began in 2008, with the aim of strengthening the research careers of female number theorists. The series introduced a novel research-mentorship model: women at all career stages, from graduate students to senior members of the community, joined forces to work in focused research groups on cutting-edge projects designed and led by experienced researchers. The goals for Women In Numbers 3 were to establish ambitious new collaborations between women in number theory, to train junior participants about topics of current importance, and to continue to build a vibrant community of women in number theory. Forty-two women attended the WIN3 workshop, including 15 senior and mid-level faculty, 15 junior faculty and postdocs, and 12 graduate students.


Coding Theory Cryptography And Related Areas

Author by : Johannes Buchmann
Languange : en
Publisher by : Springer Science & Business Media
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Description : A series of research papers on various aspects of coding theory, cryptography, and other areas, including new and unpublished results on the subjects. The book will be useful to students, researchers, professionals, and tutors interested in this area of research.


Analytic Methods In Arithmetic Geometry

Author by : Alina Bucur
Languange : en
Publisher by : American Mathematical Soc.
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Description : In the last decade or so, analytic methods have had great success in answering questions in arithmetic geometry and number theory. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry. The book contains four articles. Alina C. Cojocaru's article introduces sieving techniques to study the group structure of points of the reduction of an elliptic curve modulo a rational prime via its division fields. Harald A. Helfgott's article provides an introduction to the study of growth in groups of Lie type, with SL2(Fq) and some of its subgroups as the key examples. The article by Étienne Fouvry, Emmanuel Kowalski, Philippe Michel, and Will Sawin describes how a systematic use of the deep methods from ℓ-adic cohomology pioneered by Grothendieck and Deligne and further developed by Katz and Laumon help make progress on various classical questions from analytic number theory. The last article, by Andrew V. Sutherland, introduces Sato-Tate groups and explores their relationship with Galois representations, motivic L-functions, and Mumford-Tate groups.


Computational Arithmetic Geometry

Author by : Kristin Estella Lauter
Languange : en
Publisher by : American Mathematical Soc.
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Description : With the recent increase in available computing power, new computations are possible in many areas of arithmetic geometry. To name just a few examples, Cremona's tables of elliptic curves now go up to conductor 120,000 instead of just conductor 1,000, tables of Hilbert class fields are known for discriminant up to at least 5,000, and special values of Hilbert and Siegel modular forms can be calculated to extremely high precision. In many cases, these experimental capabilities have led to new observations and ideas for progress in the field. They have also led to natural algorithmic questions on the feasibility and efficiency of many computations, especially for the purpose of applications in cryptography. The AMS Special Session on Computational Arithmetic Geometry, held on April 29-30, 2006, in San Francisco, CA, gathered together many of the people currently working on the computational and algorithmic aspects of arithmetic geometry. This volume contains research articles related to talks given at the session. The majority of articles are devoted to various aspects of arithmetic geometry, mainly with a computational approach.


Selected Unsolved Problems In Coding Theory

Author by : David Joyner
Languange : en
Publisher by : Springer Science & Business Media
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Description : Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that still exist in coding theory. A well-established and highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a ‘noisy’ channel. Despite frequent use in a range of contexts, the subject still contains interesting unsolved problems that have resisted solution by some of the most prominent mathematicians of recent decades. Employing Sage—a free open-source mathematics software system—to illustrate ideas, this book is intended for graduate students and researchers in algebraic coding theory. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study.


Means And Their Inequalities

Author by : P.S. Bullen
Languange : en
Publisher by : Springer Science & Business Media
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Description : Approach your problems from the right end It isn't !hat they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal 0/ Fa/her 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van GuJik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fie1ds does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "complete1y integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing c1assification schemes. They draw upon wide1y different sections of mathematics.


Advances In Algebraic Geometry Codes

Author by : Edgar Mart¡nez-Moro
Languange : en
Publisher by : World Scientific
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Total Read : 59
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Description : 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.


Concise Encyclopedia Of Coding Theory

Author by : W. Cary Huffman
Languange : en
Publisher by : CRC Press
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Total Read : 92
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Description : Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research


Algebraic Function Fields And Codes

Author by : Henning Stichtenoth
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 92
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Description : 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.


Finite Fields Theory And Computation

Author by : Igor Shparlinski
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 12
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Description : This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.