Handbook Of Finite Fields PDF Download
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Author | : Gary L. Mullen |
Publisher | : CRC Press |
Total Pages | : 1048 |
Release | : 2013-06-17 |
Genre | : Computers |
ISBN | : 1439873828 |
Download Handbook of Finite Fields Book in PDF, ePub and Kindle
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 | : Gary L Mullen |
Publisher | : |
Total Pages | : 0 |
Release | : 2024-10-14 |
Genre | : Computers |
ISBN | : 9781032917320 |
Download Handbook of Finite Fields Book in PDF, ePub and Kindle
Poised to become the leading reference in the field, this definitive handbook is exclusively devoted to the theory and applications of finite fields. Edited by two renowned researchers and with more than 80 international contributors compiling state-of-the-art research, the book uses a uniform style and format throughout and each chapter is self
Author | : Dirk Hachenberger |
Publisher | : Springer Science & Business Media |
Total Pages | : 178 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 1461562694 |
Download Finite Fields Book in PDF, ePub and Kindle
Finite Fields are fundamental structures of Discrete Mathematics. They serve as basic data structures in pure disciplines like Finite Geometries and Combinatorics, and also have aroused much interest in applied disciplines like Coding Theory and Cryptography. A look at the topics of the proceed ings volume of the Third International Conference on Finite Fields and Their Applications (Glasgow, 1995) (see [18]), or at the list of references in I. E. Shparlinski's book [47] (a recent extensive survey on the Theory of Finite Fields with particular emphasis on computational aspects), shows that the area of Finite Fields goes through a tremendous development. The central topic of the present text is the famous Normal Basis Theo rem, a classical result from field theory, stating that in every finite dimen sional Galois extension E over F there exists an element w whose conjugates under the Galois group of E over F form an F-basis of E (i. e. , a normal basis of E over F; w is called free in E over F). For finite fields, the Nor mal Basis Theorem has first been proved by K. Hensel [19] in 1888. Since normal bases in finite fields in the last two decades have been proved to be very useful for doing arithmetic computations, at present, the algorithmic and explicit construction of (particular) such bases has become one of the major research topics in Finite Field Theory.
Author | : Xiang-dong Hou |
Publisher | : American Mathematical Soc. |
Total Pages | : 240 |
Release | : 2018-06-07 |
Genre | : Finite fields (Algebra) |
ISBN | : 1470442892 |
Download Lectures on Finite Fields Book in PDF, ePub and Kindle
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.
Author | : Rudolf Lidl |
Publisher | : Cambridge University Press |
Total Pages | : 784 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9780521392310 |
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This book is devoted entirely to the theory of finite fields.
Author | : Alfred J. Menezes |
Publisher | : Springer Science & Business Media |
Total Pages | : 229 |
Release | : 2013-04-17 |
Genre | : Technology & Engineering |
ISBN | : 1475722265 |
Download Applications of Finite Fields Book in PDF, ePub and Kindle
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.
Author | : Rudolf Lidl |
Publisher | : Cambridge University Press |
Total Pages | : 446 |
Release | : 1994-07-21 |
Genre | : Mathematics |
ISBN | : 9780521460941 |
Download Introduction to Finite Fields and Their Applications Book in PDF, ePub and Kindle
Presents an introduction to the theory of finite fields and some of its most important applications.
Author | : Joel V. Brawley |
Publisher | : American Mathematical Soc. |
Total Pages | : 126 |
Release | : 1989 |
Genre | : Mathematics |
ISBN | : 0821851012 |
Download Infinite Algebraic Extensions of Finite Fields Book in PDF, ePub and Kindle
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.
Author | : Kannan Soundararajan |
Publisher | : American Mathematical Society |
Total Pages | : 100 |
Release | : 2022-11-09 |
Genre | : Mathematics |
ISBN | : 1470469308 |
Download Finite Fields, with Applications to Combinatorics Book in PDF, ePub and Kindle
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.
Author | : Norman Johnson |
Publisher | : CRC Press |
Total Pages | : 884 |
Release | : 2007-02-15 |
Genre | : Mathematics |
ISBN | : 1420011146 |
Download Handbook of Finite Translation Planes Book in PDF, ePub and Kindle
The Handbook of Finite Translation Planes provides a comprehensive listing of all translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and thorough sketches of the major relevant theorems. From the methods of Andre to coordi