The first part of this book presents an introduction to the theory of finite fields, with emphasis on those aspects that are relevant for applications. The second part is devoted to a discussion of the most important applications of finite fields especially information theory, algebraic coding theory and cryptology (including some very recent material that has never before appeared in book form). There is also a chapter on applications within mathematics, such as finite geometries. combinatorics. and pseudorandom sequences. Worked-out examples and list of exercises found throughout the book make it useful as a textbook.
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Book Description
Editorial Reviews
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"...this book will continue to serve its purpose as an introduction for students, since it is devoted mainly to those parts that have a certain quality of timelessness, namely the classical theory and the standard applications of finite fields." Mathematical Reviews
--This text refers to an alternate
Hardcover
edition.
Book Description
The theory of finite fields is a branch of modern algebra that has come to the fore in recent years because of its diverse applications in such areas as combinatorics, coding theory, cryptology and the mathematical study of switching circuits. The first part of this book presents an introduction to this theory, emphasising those aspects that are relevant for application. The second part is devoted to a discussion of the most important applications of finite fields, especially to information theory, algebraic coding theory and cryptology. There is also a chapter on applications within mathematics, such as finite geometries, combinatorics and pseudo-random sequences. The book is meant to be used as a textbook: worked examples and copious exercises that range from the routine, to those giving alternative proofs of key theorems, to extensions of material covered in the text, are provided throughout.
--This text refers to an alternate
Hardcover
edition.
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Most Helpful Customer Reviews
2 of 5 people found the following review helpful:
3.0 out of 5 stars
A graduate text for Engineering students,
By A Customer
This review is from: Introduction to Finite Fields and their Applications (Hardcover)
The book is fairly dense, but it is organized as a textbook with exercises after each chapter. There is a good system of cross-indexing to allow students to skip ahead and easily locate the background material they need to review.
2 of 7 people found the following review helpful:
4.0 out of 5 stars
An undergraduate text for Mathematics students,
By A Customer
This review is from: Introduction to Finite Fields and their Applications (Hardcover)
This book covers the basics of finite field theory and its applications, but the coverage is at a level more appropriate for engineers than for mathematicians. Even for mathematicians, though, the books is an excellent introduction to the subject.Engineers may be frustrated by the lack of hardware implementation issues.
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First Sentence:
This introductory chapter contains a survey of some basic algebraic concepts that will be employed throughout the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
maximal period sequence, reciprocal characteristic polynomial, linear recurring sequence, nonzero initial state vector, canonical generator matrix, different normal bases, nontrivial partial factorization, canonical additive character, linearized polynomials, corresponding impulse response sequence, discrete exponentiation, nonconstant monic polynomials, monic linear polynomials, distinct monic irreducible factors, trivial multiplicative character, distinct monic irreducible polynomials, uniform pseudorandom numbers, multiplexed sequences, linear recurrence relation, canonical factorization, nontrivial additive character, ultimately periodic sequence, different state vectors, multiplicative order, recurring sequences Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Algebraic Foundations, Lemma Let, Prove Theorem, Use Berlekamp, Use the Zassenhaus New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This introductory chapter contains a survey of some basic algebraic concepts that will be employed throughout the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
maximal period sequence, reciprocal characteristic polynomial, linear recurring sequence, nonzero initial state vector, canonical generator matrix, different normal bases, nontrivial partial factorization, canonical additive character, linearized polynomials, corresponding impulse response sequence, discrete exponentiation, nonconstant monic polynomials, monic linear polynomials, distinct monic irreducible factors, trivial multiplicative character, distinct monic irreducible polynomials, uniform pseudorandom numbers, multiplexed sequences, linear recurrence relation, canonical factorization, nontrivial additive character, ultimately periodic sequence, different state vectors, multiplicative order, recurring sequences Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Algebraic Foundations, Lemma Let, Prove Theorem, Use Berlekamp, Use the Zassenhaus New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 50
books:
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65
books
cite this book:
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- Finite Fields, Coding Theory, and Advances in Communications and Computing (Lecture Notes in Pure and Applied Mathematics) by Gary L. Mullen in Back Matter (1), Back Matter (2), and Back Matter (3)
- Finite Fields (Encyclopedia of Mathematics and its Applications) by Rudolf Lidl in Back Matter (1), Back Matter (2), and Back Matter (3)
- Course in Number Theory and Cryptography Hb (Graduate Texts in Mathematics,) by N I Koblitz in Back Matter
- Finite Projective Spaces of Three Dimensions (Oxford Mathematical Monographs) by J. W. P. Hirschfeld in Back Matter
- Linear Groups with an Exposition of the Galois Field Theory by Leonard Eugene Dickson in Back Matter
See all 50 books this book cites
- Monte Carlo and Quasi-Monte Carlo Methods 2002: Proceedings of a Conference held at the National University of Singapore, Republic of Singapore, November 25-28, 2002 by Harald Niederreiter on page 180, page 210, and page 377
- Information Security and Privacy: 8th Australasian Conference, ACISP 2003, Wollongong, Australia, July 9-11, 2003, Proceedings (Lecture Notes in Computer Science) by Rei Safavi-Naini on page 92, and page 450
- Discrete Mathematics Using Latin Squares by Charles F. Laywine on page 240, and Back Matter
- Arithmetic of Finite Fields (Chapman & Hall/CRC Pure and Applied Mathematics) by Charles Small in Front Matter, and Back Matter
- Cellular Automata: A Discrete Universe by Andrew Ilachinski on page 243, and Back Matter
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