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Author: Robert J. McEliece
Publisher: Springer Science & Business Media
ISBN: 1461319838
Category : Technology & Engineering
Languages : en
Pages : 212
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Book Description
This book developed from a course on finite fields I gave at the University of Illinois at Urbana-Champaign in the Spring semester of 1979. The course was taught at the request of an exceptional group of graduate students (includ ing Anselm Blumer, Fred Garber, Evaggelos Geraniotis, Jim Lehnert, Wayne Stark, and Mark Wallace) who had just taken a course on coding theory from me. The theory of finite fields is the mathematical foundation of algebraic coding theory, but in coding theory courses there is never much time to give more than a "Volkswagen" treatment of them. But my 1979 students wanted a "Cadillac" treatment, and this book differs very little from the course I gave in response. Since 1979 I have used a subset of my course notes (correspond ing roughly to Chapters 1-6) as the text for my "Volkswagen" treatment of finite fields whenever I teach coding theory. There is, ironically, no coding theory anywhere in the book! If this book had a longer title it would be "Finite fields, mostly of char acteristic 2, for engineering and computer science applications. " It certainly does not pretend to cover the general theory of finite fields in the profound depth that the recent book of Lidl and Neidereitter (see the Bibliography) does.
Author: Robert J. McEliece
Publisher: Springer Science & Business Media
ISBN: 1461319838
Category : Technology & Engineering
Languages : en
Pages : 212
Get Book Here
Book Description
This book developed from a course on finite fields I gave at the University of Illinois at Urbana-Champaign in the Spring semester of 1979. The course was taught at the request of an exceptional group of graduate students (includ ing Anselm Blumer, Fred Garber, Evaggelos Geraniotis, Jim Lehnert, Wayne Stark, and Mark Wallace) who had just taken a course on coding theory from me. The theory of finite fields is the mathematical foundation of algebraic coding theory, but in coding theory courses there is never much time to give more than a "Volkswagen" treatment of them. But my 1979 students wanted a "Cadillac" treatment, and this book differs very little from the course I gave in response. Since 1979 I have used a subset of my course notes (correspond ing roughly to Chapters 1-6) as the text for my "Volkswagen" treatment of finite fields whenever I teach coding theory. There is, ironically, no coding theory anywhere in the book! If this book had a longer title it would be "Finite fields, mostly of char acteristic 2, for engineering and computer science applications. " It certainly does not pretend to cover the general theory of finite fields in the profound depth that the recent book of Lidl and Neidereitter (see the Bibliography) does.
Author: Gary L. Mullen
Publisher: CRC Press
ISBN: 1439873828
Category : Computers
Languages : en
Pages : 1048
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Book Description
Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and
Author:
Publisher: Elsevier
ISBN: 0080532950
Category : Mathematics
Languages : en
Pages : 936
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Book Description
Handbook of Algebra defines algebra as consisting of many different ideas, concepts and results. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. Each chapter of the book combines some of the features of both a graduate-level textbook and a research-level survey. This book is divided into eight sections. Section 1A focuses on linear algebra and discusses such concepts as matrix functions and equations and random matrices. Section 1B cover linear dependence and discusses matroids. Section 1D focuses on fields, Galois Theory, and algebraic number theory. Section 1F tackles generalizations of fields and related objects. Section 2A focuses on category theory, including the topos theory and categorical structures. Section 2B discusses homological algebra, cohomology, and cohomological methods in algebra. Section 3A focuses on commutative rings and algebras. Finally, Section 3B focuses on associative rings and algebras. This book will be of interest to mathematicians, logicians, and computer scientists.
Author: James (Jong Hyuk) Park
Publisher: Springer
ISBN: 3642026176
Category : Computers
Languages : en
Pages : 865
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Book Description
Welcome to the Third International Conference on Information Security and Ass- ance (ISA 2009). ISA 2009 was the most comprehensive conference focused on the various aspects of advances in information security and assurance. The concept of security and assurance is emerging rapidly as an exciting new paradigm to provide reliable and safe life services. Our conference provides a chance for academic and industry professionals to discuss recent progress in the area of communication and networking including modeling, simulation and novel applications associated with the utilization and acceptance of computing devices and systems. ISA 2009 was a succ- sor of the First International Workshop on Information Assurance in Networks (IAN 2007, Jeju-island, Korea, December, 2007), and the Second International Conference on Information Security and Assurance (ISA 2008, Busan, Korea, April 2008). The goal of this conference is to bring together researchers from academia and industry as well as practitioners to share ideas, problems and solutions relating to the multifaceted aspects of information technology. ISA 2009 contained research papers submitted by researchers from all over the world. In order to guarantee high-quality proceedings, we put extensive effort into reviewing the papers. All submissions were peer reviewed by at least three Program Committee members as well as external reviewers. As the quality of the submissions was quite high, it was extremely difficult to select the papers for oral presentation and publication in the proceedings of the conference.
Author: Albert Levi
Publisher: Springer
ISBN: 3540472436
Category : Computers
Languages : en
Pages : 1106
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Book Description
This book constitutes the refereed proceedings of the 21st International Symposium on Computer and Information Sciences, ISCIS 2006, held in Istanbul, Turkey in October 2006. The 106 revised full papers presented together with five invited lectures were carefully reviewed and selected from 606 submissions.
Author: Keith O. Geddes
Publisher: Springer Science & Business Media
ISBN: 0585332479
Category : Computers
Languages : en
Pages : 594
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Book Description
Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.
Author: Mark Goresky
Publisher: Cambridge University Press
ISBN: 1107014999
Category : Computers
Languages : en
Pages : 515
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Book Description
Describes the design, mathematical analysis and implementation of pseudo-random sequences for applications in communications, cryptography and simulations.
Author: Mikhail J. Atallah
Publisher: CRC Press
ISBN: 9781420049503
Category : Computers
Languages : en
Pages : 1328
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Book Description
Algorithms and Theory of Computation Handbook is a comprehensive collection of algorithms and data structures that also covers many theoretical issues. It offers a balanced perspective that reflects the needs of practitioners, including emphasis on applications within discussions on theoretical issues. Chapters include information on finite precision issues as well as discussion of specific algorithms where algorithmic techniques are of special importance, including graph drawing, robotics, forming a VLSI chip, vision and image processing, data compression, and cryptography. The book also presents some advanced topics in combinatorial optimization and parallel/distributed computing. • applications areas where algorithms and data structuring techniques are of special importance • graph drawing • robot algorithms • VLSI layout • vision and image processing algorithms • scheduling • electronic cash • data compression • dynamic graph algorithms • on-line algorithms • multidimensional data structures • cryptography • advanced topics in combinatorial optimization and parallel/distributed computing
Author: Constantin Enea
Publisher: Springer Nature
ISBN: 3031377036
Category : Computers
Languages : en
Pages : 473
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Book Description
The open access proceedings set LNCS 13964, 13965, 13966 constitutes the refereed proceedings of the 35th International Conference on Computer Aided Verification, CAV 2023, which was held in Paris, France, in July 2023. The 67 full papers presented in these proceedings were carefully reviewed and selected from 261 submissions. The have been organized in topical sections as follows: Part I: Automata and logic; concurrency; cyber-physical and hybrid systems; synthesis; Part II: Decision procedures; model checking; neural networks and machine learning; Part II: Probabilistic systems; security and quantum systems; software verification.
Author: Fuchun Guo
Publisher: Springer
ISBN: 3319930494
Category : Computers
Languages : en
Pages : 262
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Book Description
This monograph illustrates important notions in security reductions and essential techniques in security reductions for group-based cryptosystems. Using digital signatures and encryption as examples, the authors explain how to program correct security reductions for those cryptographic primitives. Various schemes are selected and re-proven in this book to demonstrate and exemplify correct security reductions. This book is suitable for researchers and graduate students engaged with public-key cryptography.
