Algebra for Secure and Reliable Communication Modeling

Author: Mustapha Lahyane, Edgar Martínez-Moro

Publisher: American Mathematical Soc.

ISBN: 1470410184

Category: Geometry, Algebraic

Page: 240

View: 8114

This volume contains the proceedings of the CIMPA Research School and Conference on Algebra for Secure and Reliable Communication Modeling, held from October 1-13, 2012, in Morelia, State of Michoacán, Mexico. The papers cover several aspects of the theory of coding theory and are gathered into three categories: general theory of linear codes, algebraic geometry and coding theory, and constacyclic codes over rings. The aim of this volume is to fill the gap between the theoretical part of algebraic geometry and the applications to problem solving and computational modeling in engineering, signal processing and information theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).
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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

18th International Symposium, AAECC-18, Tarragona, Sapin, June 8-12, 2009, Proceedings

Author: Maria Bras-Amorós,Tom Høholdt

Publisher: Springer Science & Business Media

ISBN: 3642021808

Category: Computers

Page: 243

View: 6063

The AAECC symposia serieswas started in 1983by Alain Poli (Toulouse), who, together with R. Desq, D. Lazardand P. Camion, organizedthe ?rst conference. OriginallytheacronymAAECCstoodfor"AppliedAlgebraandError-Correcting Codes."Overtheyearsitsmeaninghasshiftedto"AppliedAlgebra, Algebraic- gorithmsandError-CorrectingCodes,"re?ectingthegrowingimportanceofc- plexity, particularlyfor decoding algorithms.During the AAECC-12 symposium the ConferenceCommitteedecidedtoenforcethe theoryandpracticeofthe c- ing side as well as the cryptographic aspects. Algebra was conserved, as in the past, but slightly more oriented to algebraic geometry codes, ?nite ?elds, c- plexity, polynomials, andgraphs. The main topics for AAECC-18 were algebra, algebraiccomputation, codes and algebra, codes and combinatorics, modulation and codes, sequences, and cryptography. TheinvitedspeakersofthiseditionwereIwanDuursma, HenningStichtenoth, and Fernando Torres. We would like to express our deep regret for the loss of Professor Ralf Kotter, ] who recently passed away and could not be our fourth invited speaker. Except for AAECC-1 (Discrete Mathematics 56, 1985) and AAECC-7 (D- crete Applied Mathematics 33, 1991), the proceedings of all the symposia have been published in Springer'sLecture Notes in Computer Science (Vols. 228,229, 307, 356, 357, 508, 539, 673, 948, 1255, 1719, 2227, 2643, 3857, 4851). Itis apolicy ofAAECCto maintaina highscienti?c standard, comparableto that of a journal. This was made possible thanks to the many referees involved. Each submitted paper was evaluated by at least two international researchers. AAECC-18 received and refereed 50 submissions. Of these, 22 were selected for publication in these proceedings as regular papers and 7 were selected as extended abstracts.
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Algebraic-Geometric Codes

Author: M. Tsfasman,S.G. Vladut

Publisher: Springer Science & Business Media

ISBN: 9401138109

Category: Mathematics

Page: 667

View: 6965

'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d' etre of this series.
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Algebraic geometry and its applications

collections of papers from Shreeram S. Abhyankar's 60th birthday conference

Author: Shreeram Shankar Abhyankar,Chanderjit Bajaj

Publisher: Springer

ISBN: 9783540941767

Category: Mathematics

Page: 536

View: 3978

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Coding theory, design theory, group theory

proceedings of the Marshall Hall Conference

Author: Marshall Hall,Dieter Jungnickel,Scott A. Vanstone

Publisher: Wiley-Interscience

ISBN: N.A

Category: Mathematics

Page: 299

View: 341

Contains papers prepared for the 1990 multidisciplinary conference held to honor the late mathematician and researcher. Topics include applications of classic geometry to finite geometries and designs; multiple transitive permutation groups; low dimensional groups and their geometry; difference sets in 2-groups; construction of Galois groups; construction of strongly p-imbeded subgroups in finite simple groups; Hall triple systems, Fisher spaces and 3-transposition groups; explicit embeddings in finitely generated groups; 2-transitive and flag transitive designs; efficient representations of perm groups; codes and combinatorial designs; optimal normal bases for finite fields; vector space designs from quadratic forms and inequalities; primitive permutation groups, graphs and relation algebras; large sets of ordered designs, orthogonal 1-factorizations and hyperovals; algebraic integers all of whose algebraic conjugates have the same absolute value.
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Algebraic Geometry in Coding Theory and Cryptography

Author: Harald Niederreiter,Chaoping Xing

Publisher: Princeton University Press

ISBN: 9781400831302

Category: Mathematics

Page: 272

View: 4509

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
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Algebraic Geometry and Its Applications

Руды Ордена Ленина Математического Института Имени В.А.Стеклова

Author: Sergeĭ Mikhaĭlovich Nikolʹskiĭ,E. A. Volkov

Publisher: American Mathematical Soc.

ISBN: 9780821830925

Category: Mathematics

Page: 251

View: 4553

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Topics in Geometry, Coding Theory and Cryptography

Author: Arnaldo Garcia,Henning Stichtenoth

Publisher: Springer Science & Business Media

ISBN: 1402053347

Category: Mathematics

Page: 201

View: 3453

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.
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Algebraic Geometry and its Applications

Proceedings of the 8th Algebraic Geometry Conference, Yaroslavl’ 1992. A Publication from the Steklov Institute of Mathematics. Adviser: Armen Sergeev

Author: Alexander Tikhomirov,Andrej Tyurin

Publisher: Springer Science & Business Media

ISBN: 3322993426

Category: Technology & Engineering

Page: 251

View: 6015

This volume contains 18 papers at the Algebraic Geometry Conference, Yaroslavl', August 10-14, 1992. These conferences in algebraic geometry have a great tradition in Russia and are helt since 1979 in Yaroslavl' every second year. The present conference, the eighth one, was the first in which several foreign mathematicians participated. From the Russian side, there was a large group of specialists in algebraic geometry and related fields (invariant theory, topology of manifolds, theory of categories, mathematical physics etc.). Lectures on modern directions in algebraic geometry, such as the theory of exceptional bundles and helices on algebraic varieties, moduli of vector bundles on algebraic surfaces with applications to Donaldson's theory, geometry of Hilbert schemes of points, twistor spaces and applications to string theory, and more traditional areas, such as birational geometry of manifolds, adjunction theory, Hodge theory, problems of rationality in the invariant theory, topology of complex algebraic varieties, and others are contained in this volume.
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Algebraic Codes on Lines, Planes, and Curves

An Engineering Approach

Author: Richard E. Blahut

Publisher: Cambridge University Press

ISBN: 1139469460

Category: Technology & Engineering

Page: N.A

View: 5712

The past few years have witnessed significant developments in algebraic coding theory. This book provides an advanced treatment of the subject from an engineering perspective, covering the basic principles and their application in communications and signal processing. Emphasis is on codes defined on the line, on the plane, and on curves, with the core ideas presented using commutative algebra and computational algebraic geometry made accessible using the Fourier transform. Starting with codes defined on a line, a background framework is established upon which the later chapters concerning codes on planes, and on curves, are developed. The decoding algorithms are developed using the standard engineering approach applied to those of Reed-Solomon codes, enabling them to be evaluated against practical applications. Integrating recent developments in the field into the classical treatment of algebraic coding, this is an invaluable resource for graduate students and researchers in telecommunications and applied mathematics.
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Theory and Applications of Models of Computation

9th Annual Conference, TAMC 2012, Beijing, China, May 16-21, 2012. Proceedings

Author: Manindra Agrawal,Barry S. Cooper,Angsheng Li

Publisher: Springer

ISBN: 3642299520

Category: Computers

Page: 622

View: 9156

This book constitutes the refereed proceedings of the 9th International Conference on Theory and Applications of Models of Computation, TAMC 2012, held in Beijing, China, in May 2012. The conference was combined with the Turing Lectures 2012, dedicated to celebrating Alan Turing’s unique impact on mathematics, computing, computer science, informatics, morphogenesis, philosophy, and the wider scientific world. Eight Turing Lectures were given at the TAMC 2012. The 40 revised full papers presented together with invited talks were carefully reviewed and selected from 86 submissions. The papers address 4 special sessions at TAMC 2012 which were algorithms and information in networks, complexity and cryptography, models of computing and networking, programming and verification.
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Geometric Algebra with Applications in Science and Engineering

Author: Eduardo Bayro Corrochano,Garret Sobczyk

Publisher: Springer Science & Business Media

ISBN: 9780817641993

Category: Computers

Page: 592

View: 2253

This book is addressed to a broad audience of cyberneticists, computer scientists, engineers, applied physicists and applied mathematicians. The book offers several examples to clarify the importance of geometric algebra in signal and image processing, filtering and neural computing, computer vision, robotics and geometric physics. The contributions of this book will help the reader to greater understand the potential of geometric algebra for the design and implementation of real time artifical systems.
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Applications of Computational Algebraic Geometry

American Mathematical Society Short Course, January 6-7, 1997, San Diego, California

Author: Dinesh N. Manocha

Publisher: American Mathematical Soc.

ISBN: 0821807501

Category: Mathematics

Page: 172

View: 1907

This book introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Grobner 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 Grobner 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 the book assume no previous acquaintance with the material.
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Applied algebra, algebraic algorithms and error-correcting codes

10th international symposium, AAECC-10, San Juan de Puerto, Puerto Rico, May 10-14, 1993 : proceedings

Author: Gérard Cohen,Teo Mora

Publisher: Springer Verlag

ISBN: N.A

Category: Computers

Page: 354

View: 7568

"This volume is the proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 10),held in Puerto Rico, May 1993. The aim of the AAECC meetings is to attract high-level research papers and to encourage cross-fertilization among different areas which share the use of algebraic methods and techniques for applications in the sciences of computing, communications, and engineering. The AAECC symposia are mainly devoted to research in coding theory and computer algebra. The theoryof error-correcting codes deals with the transmission of information in the presence of noise. Coding is the systematic use of redundancy in theformation of the messages to be sent so as to enable the recovery of the information present originally after it has been corrupted by (not too much)noise. Computer algebra is devoted to the investigation of algorithms, computational methods, software systems and computer languages, oriented to scientific computations performed on exact and often symbolic data, by manipulating formal expressions by means of the algebraic rules they satisfy. Questions of complexity and cryptography are naturally linked with both coding theory and computer algebra and represent an important share of the area covered by AAECC."--PUBLISHER'S WEBSITE.
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Codes and Algebraic Curves

Author: Oliver Pretzel

Publisher: Clarendon Press

ISBN: 0191589047

Category: Mathematics

Page: 208

View: 6545

The geometry of curves has fascinated mathematicians for 2500 years, and the theory has become highly abstract. Recently links have been made with the subject of error correction, leading to the creation of geometric Goppa codes, a new and important area of coding theory. This book is an updated and extended version of the last part of the successful book Error-Correcting Codes and Finite Fields. It provides an elementary introduction to Goppa codes, and includes many examples, calculations, and applications. The book is in two parts with an emphasis on motivation, and applications of the theory take precedence over proofs of theorems. The formal theory is, however, provided in the second part of the book, and several of the concepts and proofs have been simplified without sacrificing rigour.
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Algebraic K-Theory and Its Applications

Author: Jonathan Rosenberg

Publisher: Springer Science & Business Media

ISBN: 1461243149

Category: Mathematics

Page: 394

View: 3151

Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.
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