Finite Fields: Theory, Applications and Algorithms PDF Download
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: Theory, Applications and Algorithms PDF full book. Access full book title Finite Fields: Theory, Applications and Algorithms by Ronald Cleveland Mullin. Download full books in PDF and EPUB format.
Author: Ronald Cleveland Mullin
Publisher: American Mathematical Soc.
ISBN: 0821808176
Category : Mathematics
Languages : en
Pages : 258
Get Book Here
Book Description
The Ontario conference drew workers from theoretical, applied, and algorithm finite field theory to share their recent findings applying finite fields to such areas as number theory, algebra, and algebraic geometry. The 21 topics include actions of linearized polynomials on the algebraic closure of a finite field, kernels and defaults, computing zeta functions over finite fields, and the state complexity of some long codes. No index. Member prices are $39 for institutions and $29 for individuals. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Ronald Cleveland Mullin
Publisher: American Mathematical Soc.
ISBN: 0821808176
Category : Mathematics
Languages : en
Pages : 258
Get Book Here
Book Description
The Ontario conference drew workers from theoretical, applied, and algorithm finite field theory to share their recent findings applying finite fields to such areas as number theory, algebra, and algebraic geometry. The 21 topics include actions of linearized polynomials on the algebraic closure of a finite field, kernels and defaults, computing zeta functions over finite fields, and the state complexity of some long codes. No index. Member prices are $39 for institutions and $29 for individuals. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Gary L. Mullen
Publisher: American Mathematical Soc.
ISBN: 0821851837
Category : Mathematics
Languages : en
Pages : 434
Get Book Here
Book Description
Because of their applications in so many diverse areas, finite fields continue to play increasingly important roles in various branches of modern mathematics, including number theory, algebra, and algebraic geometry, as well as in computer science, information theory, statistics, and engineering. Computational and algorithmic aspects of finite field problems also continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. Among the topics treated are theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory, and algorithms related to finite fields. Also included is a list of open problems and conjectures. This volume is an excellent reference for applied and research mathematicians as well as specialists and graduate students in information theory, computer science, and electrical engineering.
Author: Igor Shparlinski
Publisher: Springer Science & Business Media
ISBN: 940111806X
Category : Mathematics
Languages : en
Pages : 253
Get Book Here
Book Description
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: Gary L. Mullen
Publisher: American Mathematical Soc.
ISBN: 0821844180
Category : Computers
Languages : en
Pages : 190
Get Book Here
Book Description
Finite fields Combinatorics Algebraic coding theory Cryptography Background in number theory and abstract algebra Hints for selected exercises References Index.
Author: Alfred J. Menezes
Publisher: Springer Science & Business Media
ISBN: 1475722265
Category : Technology & Engineering
Languages : en
Pages : 229
Get Book Here
Book Description
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: Gary L. Mullen
Publisher: CRC Press
ISBN: 1439873828
Category : Computers
Languages : en
Pages : 1048
Get Book Here
Book Description
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
ISBN: 9780521392310
Category : Mathematics
Languages : en
Pages : 784
Get Book Here
Book Description
This book is devoted entirely to the theory of finite fields.
Author: Igor Shparlinski
Publisher: Springer Science & Business Media
ISBN: 940159239X
Category : Mathematics
Languages : en
Pages : 532
Get Book Here
Book Description
This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the 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 areas of mathematics. For completeness we in clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.
Author: Kai-Uwe Schmidt
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110641968
Category : Mathematics
Languages : en
Pages : 459
Get Book Here
Book Description
Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.
Author: Robert J. McEliece
Publisher: Springer Science & Business Media
ISBN: 1461319838
Category : Technology & Engineering
Languages : en
Pages : 212
Get Book Here
Book Description
This book developed from a course on finite fields I gave at the University of Illinois at Urbana-Champaign in the Spring semester of 1979. The course was taught at the request of an exceptional group of graduate students (includ ing Anselm Blumer, Fred Garber, Evaggelos Geraniotis, Jim Lehnert, Wayne Stark, and Mark Wallace) who had just taken a course on coding theory from me. The theory of finite fields is the mathematical foundation of algebraic coding theory, but in coding theory courses there is never much time to give more than a "Volkswagen" treatment of them. But my 1979 students wanted a "Cadillac" treatment, and this book differs very little from the course I gave in response. Since 1979 I have used a subset of my course notes (correspond ing roughly to Chapters 1-6) as the text for my "Volkswagen" treatment of finite fields whenever I teach coding theory. There is, ironically, no coding theory anywhere in the book! If this book had a longer title it would be "Finite fields, mostly of char acteristic 2, for engineering and computer science applications. " It certainly does not pretend to cover the general theory of finite fields in the profound depth that the recent book of Lidl and Neidereitter (see the Bibliography) does.
