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Finite Fields And Galois Rings

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Finite Fields And Galois Rings

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Author : Zhe-xian Wan
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-09-13

Finite Fields And Galois Rings written by Zhe-xian Wan and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-13 with Mathematics categories.

A large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer science and other fields. The remaining part can be used as references for specialists. Explicit construction and computation of finite fields are emphasized. In particular, the construction of irreducible polynomials and normal basis of finite field is included. A detailed treatment of optimal normal basis and Galoi's rings is included. It is the first time that the galois rings are in book form.

Lectures On Finite Fields And Galois Rings

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Author : Zhe-Xian Wan
language : en
Publisher: World Scientific
Release Date : 2003

Lectures On Finite Fields And Galois Rings written by Zhe-Xian Wan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.

Lectures On Finite Fields And Galois Rings

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Author : Zhe-xian Wan
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-08-12

Lectures On Finite Fields And Galois Rings written by Zhe-xian Wan and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-12 with Mathematics categories.

Galois Fields And Galois Rings Made Easy

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Author : Maurice Kibler
language : en
Publisher: Elsevier
Release Date : 2017-09-22

Galois Fields And Galois Rings Made Easy written by Maurice Kibler and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-22 with Mathematics categories.

This book constitutes an elementary introduction to rings and fields, in particular Galois rings and Galois fields, with regard to their application to the theory of quantum information, a field at the crossroads of quantum physics, discrete mathematics and informatics.The existing literature on rings and fields is primarily mathematical. There are a great number of excellent books on the theory of rings and fields written by and for mathematicians, but these can be difficult for physicists and chemists to access.This book offers an introduction to rings and fields with numerous examples. It contains an application to the construction of mutually unbiased bases of pivotal importance in quantum information. It is intended for graduate and undergraduate students and researchers in physics, mathematical physics and quantum chemistry (especially in the domains of advanced quantum mechanics, quantum optics, quantum information theory, classical and quantum computing, and computer engineering).Although the book is not written for mathematicians, given the large number of examples discussed, it may also be of interest to undergraduate students in mathematics. - Contains numerous examples that accompany the text - Includes an important chapter on mutually unbiased bases - Helps physicists and theoretical chemists understand this area of mathematics

Finite Commutative Rings And Their Applications

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Author : Gilberto Bini
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Finite Commutative Rings And Their Applications written by Gilberto Bini 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 2012-12-06 with Technology & Engineering categories.

Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.

Finite Fields And Applications

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Author : Gary L. Mullen
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Finite Fields And Applications written by Gary L. Mullen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Computers categories.

This volume contains the proceedings of the Eighth International Conference on Finite Fields and Applications, held in Melbourne, Australia, July 9-13, 2007. It contains 5 invited survey papers as well as original research articles covering various theoretical and applied areas related to finite fields.Finite fields, and the computational and algorithmic aspects of finite field problems, continue to grow in importance and interest in the mathematical and computer science communities because of their applications in so many diverse areas. In particular, finite fields now play very important roles in number theory, algebra, and algebraic geometry, as well as in computer science, statistics, and engineering. Areas of application include algebraic coding theory, cryptology, and combinatorialdesign theory.

Finite Fields And Applications

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Author : Stephen Cohen
language : en
Publisher: Cambridge University Press
Release Date : 1996-09-28

Finite Fields And Applications written by Stephen Cohen 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 1996-09-28 with Mathematics categories.

Finite fields are algebraic structures in which there is much research interest. This book gives a state-of-the-art account of finite fields and their applications in communications (coding theory, cryptology), combinatorics, design theory, quasirandom points, algorithms and their complexity. Typically, theory and application are tightly interwoven in the survey articles and original research papers included here. The book also demonstrates interconnections with other branches of pure mathematics such as number theory, group theory and algebraic geometry. This volume is an invaluable resource for any researcher in finite fields or related areas.

Galois Theories

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Author : Francis Borceux
language : en
Publisher: Cambridge University Press
Release Date : 2001-02-22

Galois Theories written by Francis Borceux 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 2001-02-22 with Mathematics categories.

Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read.

Galois Theory Through Exercises

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Author : Juliusz Brzeziński
language : en
Publisher: Springer
Release Date : 2018-03-21

Galois Theory Through Exercises written by Juliusz Brzeziński and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Mathematics categories.

This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.

Finite Fields And Applications

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Author : Dieter Jungnickel
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-03-20

Finite Fields And Applications written by Dieter Jungnickel 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 2001-03-20 with Mathematics categories.

This volume represents the refereed proceedings of the Fifth International Conference on Finite Fields and Applications (F q5) held at the University of Augsburg (Germany) from August 2-6, 1999, and hosted by the Department of Mathematics. The conference continued a series of biennial international conferences on finite fields, following earlier conferences at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University ofGlasgow (Scotland) in July 1995, and the University ofWaterloo (Canada) in August 1997. The Organizing Committee of F q5 comprised Thomas Beth (University ofKarlsruhe), Stephen D. Cohen (University of Glasgow), Dieter Jungnickel (University of Augsburg, Chairman), Alfred Menezes (University of Waterloo), Gary L. Mullen (Pennsylvania State University), Ronald C. Mullin (University of Waterloo), Harald Niederreiter (Austrian Academy of Sciences), and Alexander Pott (University of Magdeburg). The program ofthe conference consisted offour full days and one halfday ofsessions, with 11 invited plenary talks andover80contributedtalks that re- quired three parallel sessions. This documents the steadily increasing interest in finite fields and their applications. Finite fields have an inherently fasci- nating structure and they are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields.

Finite Fields And Galois Rings

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