Handbook Of Finite Fields
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Handbook Of Finite Fields
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Author : Gary L. Mullen
language : en
Publisher: CRC Press
Release Date : 2013-06-17
Handbook Of Finite Fields written by Gary L. Mullen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-17 with Computers categories.
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
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: 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.
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. Errata(s) Errata
Finite Fields And Galois Rings
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Author : Wan Zhe-Xian
language : en
Publisher:
Release Date : 2011
Finite Fields And Galois Rings written by Wan Zhe-Xian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Lectures On Finite Fields
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Author : Xiang-dong Hou
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-06-07
Lectures On Finite Fields written by Xiang-dong Hou 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 2018-06-07 with Finite fields (Algebra) categories.
The theory of finite fields encompasses algebra, combinatorics, and number theory and has furnished widespread applications in other areas of mathematics and computer science. This book is a collection of selected topics in the theory of finite fields and related areas. The topics include basic facts about finite fields, polynomials over finite fields, Gauss sums, algebraic number theory and cyclotomic fields, zeros of polynomials over finite fields, and classical groups over finite fields. The book is mostly self-contained, and the material covered is accessible to readers with the knowledge of graduate algebra; the only exception is a section on function fields. Each chapter is supplied with a set of exercises. The book can be adopted as a text for a second year graduate course or used as a reference by researchers.
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 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.
Infinite Algebraic Extensions Of Finite Fields
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Author : Joel V. Brawley
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Infinite Algebraic Extensions Of Finite Fields written by Joel V. Brawley 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 1989 with Mathematics categories.
Over the last several decades there has been a renewed interest in finite field theory, partly as a result of important applications in a number of diverse areas such as electronic communications, coding theory, combinatorics, designs, finite geometries, cryptography, and other portions of discrete mathematics. In addition, a number of recent books have been devoted to the subject. Despite the resurgence in interest, it is not widely known that many results concerning finite fields have natural generalizations to abritrary algebraic extensions of finite fields. The purpose of this book is to describe these generalizations. After an introductory chapter surveying pertinent results about finite fields, the book describes the lattice structure of fields between the finite field $GF(q)$ and its algebraic closure $\Gamma (q)$. The authors introduce a notion, due to Steinitz, of an extended positive integer $N$ which includes each ordinary positive integer $n$ as a special case. With the aid of these Steinitz numbers, the algebraic extensions of $GF(q)$ are represented by symbols of the form $GF(q^N)$. When $N$ is an ordinary integer $n$, this notation agrees with the usual notation $GF(q^n)$ for a dimension $n$ extension of $GF(q)$. The authors then show that many of the finite field results concerning $GF(q^n)$ are also true for $GF(q^N)$. One chapter is devoted to giving explicit algorithms for computing in several of the infinite fields $GF(q^N)$ using the notion of an explicit basis for $GF(q^N)$ over $GF(q)$. Another chapter considers polynomials and polynomial-like functions on $GF(q^N)$ and contains a description of several classes of permutation polynomials, including the $q$-polynomials and the Dickson polynomials. Also included is a brief chapter describing two of many potential applications. Aimed at the level of a beginning graduate student or advanced undergraduate, this book could serve well as a supplementary text for a course in finite field theory.
Finite Fields With Applications To Combinatorics
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Author : Kannan Soundararajan
language : en
Publisher: American Mathematical Society
Release Date : 2022-11-09
Finite Fields With Applications To Combinatorics written by Kannan Soundararajan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-09 with Mathematics categories.
This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.
Finite Fields
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Author : Rudolf Lidl
language : en
Publisher:
Release Date : 1996
Finite Fields 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 1996 with Electronic books categories.
This book is devoted entirely to the theory of finite fields.