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Finite Fields: Theory and Computation: The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography: 477 - Brossura

 
9789048152032: Finite Fields: Theory and Computation: The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography: 477

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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.

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Recensione

`...the book can yet be highly recommended as encyclopaedia on these topics, in particular because many Russian papers are incorporated which are hardly accessible.'
Monatschafte für Mathematik, 132:1 (2001)

Contenuti

Preface. Acknowledgments. Notation. Introduction. Links flowchart. 1. Polynomial Factorization. 2. Finding Irreducible and Primitive Polynomials. 3. The Distribution of Irreducible, Primitive and Other Special Polynomials and Matrices. 4. Bases and Computation in Finite Fields. 5. Coding Theory and Algebraic Curves. 6. Elliptic Curves. 7. Recurrence Sequences in Finite Fields and Cyclic Linear Codes. 8. Finite Fields and Discrete Mathematics. 9. Congruences. 10. Some Related Problems. Appendix 1. Appendix 2. Appendix 3. References. Index.

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9780792356622: Finite Fields: Theory and Computation : The Meeting Point of Number Theory, Computer Science, Coding Theory, and Cryptography: 477

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ISBN 10:  0792356624 ISBN 13:  9780792356622
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 544 pp. Englisch. Codice articolo 9789048152032

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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 point. Codice articolo 5819062

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Paperback. Condizione: new. Paperback. This book provides an exhaustive survey of the most recent achievements in the theory and applications of finite fields and in many related areas such as algebraic number theory, theoretical computer science, coding theory and cryptography. Topics treated include polynomial factorization over finite fields, the finding and distribution of irreducible primitive and other special polynomials, constructing special bases of extensions of finite fields, curves and exponential sums, and linear recurrent sequences. Besides a general overview of the area, its results and methods, it suggests a number of interesting research problems of various levels of difficulty. The volume concludes with an impressive bibliographical section containing more than 2300 references. Audience: This work will be of interest to graduate students and researchers in field theory and polynomials, number theory, symbolic computation, symbolic/algebraic manipulation, and coding theory. 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 inA clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generA 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, CodA 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 US Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9789048152032

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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 544 pp. Englisch. Codice articolo 9789048152032

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