Introduction To Finite Fields And Their Applications
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Introduction To Finite Fields And Their Applications
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Author : Rudolf Lidl
language : en
Publisher: Cambridge University Press
Release Date : 1994-07-21
Introduction To Finite Fields And Their Applications written by Rudolf Lidl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-07-21 with Mathematics categories.
Presents an introduction to the theory of finite fields and some of its most important applications.
Introduction To Finite Fields And Their Applications
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Author : R. Lidl
language : en
Publisher:
Release Date : 1986
Introduction To Finite Fields And Their Applications written by R. Lidl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Finite Fields
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Author : Rudolf Lidl
language : en
Publisher: Cambridge University Press
Release Date : 1997
Finite Fields written by Rudolf Lidl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
This book is devoted entirely to the theory of finite fields.
Introduction To Finite Fields And Their Applications
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Author : Rudolf Lidl
language : en
Publisher:
Release Date : 1986
Introduction To Finite Fields And Their Applications written by Rudolf Lidl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
The first part of this book presents an introduction to the theory of finite fields, with emphasis on those aspects that are relevant for applications. The second part is devoted to a discussion of the most important applications of finite fields especially information theory, algebraic coding theory and cryptology (including some very recent material that has never before appeared in book form). There is also a chapter on applications within mathematics, such as finite geometries. combinatorics. and pseudorandom sequences. Worked-out examples and list of exercises found throughout the book make it useful as a textbook.
Finite Fields And Their Applications
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Author : Pascale Charpin
language : en
Publisher: Walter de Gruyter
Release Date : 2013-05-28
Finite Fields And Their Applications written by Pascale Charpin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-28 with Mathematics categories.
This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas: Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums. Chapters 3, 5, and 6 deal with polynomials over finite fields. Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively. Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation. Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.
Finite Fields And Their Applications
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Author : James A. Davis
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-10-26
Finite Fields And Their Applications written by James A. Davis and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-26 with Mathematics categories.
The volume covers wide-ranging topics from Theory: structure of finite fields, normal bases, polynomials, function fields, APN functions. Computation: algorithms and complexity, polynomial factorization, decomposition and irreducibility testing, sequences and functions. Applications: algebraic coding theory, cryptography, algebraic geometry over finite fields, finite incidence geometry, designs, combinatorics, quantum information science.
Applications Of Finite Fields
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Author : Alfred J. Menezes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Applications Of Finite Fields written by Alfred J. Menezes 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 Technology & Engineering categories.
The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches in mathematics. Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. The purpose of this book is to introduce the reader to some of these recent developments. It should be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. We shall focus our attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, we have not attempted to be encyclopedic. Among the topics studied are different methods of representing the elements of a finite field (including normal bases and optimal normal bases), algorithms for factoring polynomials over finite fields, methods for constructing irreducible polynomials, the discrete logarithm problem and its implications to cryptography, the use of elliptic curves in constructing public key cryptosystems, and the uses of algebraic geometry in constructing good error-correcting codes. To limit the size of the volume we have been forced to omit some important applications of finite fields. Some of these missing applications are briefly mentioned in the Appendix along with some key references.
Finite Fields
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Author : Lidl
language : en
Publisher: Cambridge University Press
Release Date : 1984-12-28
Finite Fields written by Lidl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-28 with Mathematics categories.
The theory of finite fields is a branch of modern algebra that has come to the fore in the last fifty years because of its diverse applications in such areas as combinatorics, coding theory and the mathematical study of switching circuits. This book, the first one devoted entirely to this theory, provides comprehensive coverage of the literature on finite fields and their applications. Extensive bibliographical notes at the end of each chapter give a historical survey of the development of the subject. Worked examples and lists of exercises found throughout the book make it useful as a text for advanced level courses.
Introduction To Modern Algebra And Its Applications
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Author : Nadiya Gubareni
language : en
Publisher: CRC Press
Release Date : 2021-06-23
Introduction To Modern Algebra And Its Applications written by Nadiya Gubareni and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-23 with Mathematics categories.
The book provides an introduction to modern abstract algebra and its applications. It covers all major topics of classical theory of numbers, groups, rings, fields and finite dimensional algebras. The book also provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. In particular, it considers algorithm RSA, secret sharing algorithms, Diffie-Hellman Scheme and ElGamal cryptosystem based on discrete logarithm problem. It also presents Buchberger’s algorithm which is one of the important algorithms for constructing Gröbner basis. Key Features: Covers all major topics of classical theory of modern abstract algebra such as groups, rings and fields and their applications. In addition it provides the introduction to the number theory, theory of finite fields, finite dimensional algebras and their applications. Provides interesting and important modern applications in such subjects as Cryptography, Coding Theory, Computer Science and Physics. Presents numerous examples illustrating the theory and applications. It is also filled with a number of exercises of various difficulty. Describes in detail the construction of the Cayley-Dickson construction for finite dimensional algebras, in particular, algebras of quaternions and octonions and gives their applications in the number theory and computer graphics.
Arithmetic Of Finite Fields
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Author : Charles Small
language : en
Publisher: CRC Press
Release Date : 1991-04-24
Arithmetic Of Finite Fields written by Charles Small and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-04-24 with Mathematics categories.
Text for a one-semester course at the advanced undergraduate/beginning graduate level, or reference for algebraists and mathematicians interested in algebra, algebraic geometry, and number theory, examines counting or estimating numbers of solutions of equations in finite fields concentrating on top