Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Finite Fields And Their Applications PDF full book. Access full book title Finite Fields And Their Applications.
| Author | : Rudolf Lidl |
| Publisher | : Cambridge University Press |
| Total Pages | : 784 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9780521392310 |
This book is devoted entirely to the theory of finite fields.
| Author | : Gary L. Mullen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 190 |
| Release | : 2007 |
| Genre | : Computers |
| ISBN | : 0821844180 |
Finite fields Combinatorics Algebraic coding theory Cryptography Background in number theory and abstract algebra Hints for selected exercises References Index.
| Author | : Gary L. Mullen |
| Publisher | : CRC Press |
| Total Pages | : 1048 |
| Release | : 2013-06-17 |
| Genre | : Computers |
| ISBN | : 1439873828 |
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 | : Rudolf Lidl |
| Publisher | : Cambridge University Press |
| Total Pages | : 446 |
| Release | : 1994-07-21 |
| Genre | : Mathematics |
| ISBN | : 9780521460941 |
Presents an introduction to the theory of finite fields and some of its most important applications.
| Author | : Pascale Charpin |
| Publisher | : Walter de Gruyter |
| Total Pages | : 288 |
| Release | : 2013-05-28 |
| Genre | : Mathematics |
| ISBN | : 3110283603 |
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.
| Author | : Alfred J. Menezes |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 229 |
| Release | : 2013-04-17 |
| Genre | : Technology & Engineering |
| ISBN | : 1475722265 |
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 | : Xiang-dong Hou |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 240 |
| Release | : 2018-06-07 |
| Genre | : Finite fields (Algebra) |
| ISBN | : 1470442892 |
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 | : Kai-Uwe Schmidt |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 506 |
| Release | : 2019-07-08 |
| Genre | : Mathematics |
| ISBN | : 3110641968 |
The series is devoted to the publication of high-level monographs, surveys and proceedings which cover the whole spectrum of computational and applied mathematics. The books of this series are addressed to both specialists and advanced students. Interested authors may submit book proposals to the Managing Editor or to any member of the Editorial Board. Managing EditorUlrich Langer, Johannes Kepler University Linz, Austria Editorial BoardHansj rg Albrecher, University of Lausanne, SwitzerlandRonald H. W. Hoppe, University of Houston, USAKarl Kunisch, RICAM, Linz, Austria; University of Graz, AustriaHarald Niederreiter, RICAM, Linz, AustriaChristian Schmeiser, University of Vienna, Austria
| Author | : Igor Shparlinski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 253 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 940111806X |
This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, 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 araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.
| Author | : Harald Niederreiter |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 254 |
| Release | : 2014-08-20 |
| Genre | : Mathematics |
| ISBN | : 3110317915 |
Algebra and number theory have always been counted among the most beautiful and fundamental mathematical areas with deep proofs and elegant results. However, for a long time they were not considered of any substantial importance for real-life applications. This has dramatically changed with the appearance of new topics such as modern cryptography, coding theory, and wireless communication. Nowadays we find applications of algebra and number theory frequently in our daily life. We mention security and error detection for internet banking, check digit systems and the bar code, GPS and radar systems, pricing options at a stock market, and noise suppression on mobile phones as most common examples. This book collects the results of the workshops "Applications of algebraic curves" and "Applications of finite fields" of the RICAM Special Semester 2013. These workshops brought together the most prominent researchers in the area of finite fields and their applications around the world. They address old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.
