Kindly note that we have put a lot of effort into researching the best books on Finite Fields and Their Applications subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Finite Fields and Their Applications" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.
1. “Finite Fields” by Rudolf Lidl and Harald Niederreiter
Book Review: This book covers various areas like combinatorics, coding theory, cryptology, switching circuits and so on. The book provides an introduction about the theory of these aspects thereby stressing the aspects relevant to the application. The book also contains chapters on finite field applications, information theory, algebraic coding theory, cryptology, finite geometries, combinatorics and pseudo random sequences. The book is a very good textbook at graduate level along with worked examples and exercises.


2. “Coding and Information Theory” by Steven Roman
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Book Review: This book is a very nice textbook in the field of information and coding theory at the graduate and undergraduate level.It covers the fundamental issues in the field of probability and modern algebra. The book also covers the topics of shannon’s noisy coding theorem, hamming and reed muller codes, finite fields, cyclic codes, BCH, reedsolomon, justesen, goppa and quadratic residue codes. The book also contains certain topics from the field of modern algebra.


3. “Introduction to Finite Fields and their Applications” by R Lidl and H Niederreiter
Book Review: This book covers various areas like combinatorics, coding theory, cryptology, switching circuits and so on. The book provides an introduction about the theory of these aspects thereby stressing the aspects relevant to the application. The book also contains chapters on finite field applications, information theory, algebraic coding theory, cryptology, finite geometries, combinatorics and pseudo random sequences. The book is a very good textbook at graduate level along with worked examples and exercises.


4. “Finite Fields and Their Applications: Character Sums and Polynomials” by Pascale Charpin and Alexander Pott
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“Finite Fields and their Applications: Character Sums and Polynomials” Book Review: This book presents the recent research carried out in sequences, polynomials, and character sums under the unified framework of character theory. The initial chapters deal with polynomials over finite fields as well as sequences constructed via characters and analyzed using bounds on character sums. A separate chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. Quasirandom points are discussed to elaborate its applications in numerical integration using quasiMonte Carlo methods and simulation. The book also examines problems related to coding theory studied via finite geometry and additive combinatorics.


5. “Finite Fields and Applications: 7th International Conference, Fq7 Toulouse, France, May 59, 2003 Revised Papers” by Mullen Poli
“Finite Fields and Applications: 7th International Conference, Fq7, Toulouse, France, May 59, 2003, Revised Paper” Book Review: This book contains 19 selected papers from the refereed proceedings of the 7th International Conference on Finite Fields and Applications, Fq7, held in Toulouse, France, in May 2003. The book starts with the discussion of Weierstrass semigroups, Galois rings, hyperelliptic curves, polynomial irreducibility, pseudorandom number sequences, permutation polynomials, and random polynomials. Subsequent chapters deal with matrices, function fields, ramified towers, BCH codes, cyclic codes, primitive polynomials, covering sequences, and cyclic decompositions.


6. “Finite Fields with Applications to Coding Theory, Cryptography and Related Areas” by Gary L Mullen and Henning Stichtenoth
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“Finite Fields with Applications to Coding Theory, Cryptography and Related Areas” Book Review: This book contains the proceedings of the Sixth International Conference on Finite Fields and Applications, Fq6, held in Oaxaca, Mexico, from 2226 May 2001. The book discusses the fundamental concepts of finite fields as well as their applications in the real world. The importance of finite fields in discrete mathematics, cryptography, coding theory, design theory, finite & algebraic geometry, scientific computation, and other related areas are thoroughly explored.


7. “Finite Fields and Applications” by H Niederreiter and Dieter Jungnickel
“Finite Fields and Applications” Book Review: This book contains the proceedings of the Fifth International Conference on Finite Fields and Applications Fq5 held at the University of Augsburg, Germany, from August 26, 1999. It presents numerous updated research articles on the theoretical and practical aspects of finite fields. A wide range of applications, starting from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing, are all covered in great detail.


8. “Rational Points on Curves Over Finite Fields: Theory And Applications” by J W S Cassels and Harald Niederreiter
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“Rational Points on Curves Over Finite Fields: Theory And Applications” Book Review: This book offers a detailed treatment of rational points on algebraic curves over finite fields. The book successfully summarizes the theoretical work on algebraic curves over finite fields with numerous rational points. The book also discusses the applications of this theory such as algebraic coding theory in the field of information theory and construction of lowdiscrepancy sequences in the field of computational mathematics. The authors have given the first systematic treatment of this material in this book. Algebraic geometers and coding theorists will find this book useful.


9. “Handbook of Finite Fields” by Mullen Panario
“Handbook of Finite Fields” Book Review: This selfcontained book presents the foundational concepts as well as the recent research conducted in finite fields in a comprehensive manner. The book begins by acquainting the reader with the history of finite fields. The theoretical properties of finite fields are then covered in detail, including polynomials, algorithms, curves, special functions, sequences, and related computational aspects. A comprehensive index along with 3,000 references is provided for thorough research of any topic. Numerous mathematical and practical applications of finite fields in quantum information theory, algebraic coding theory, cryptographic systems, combinatorics, engineering, biology, etc. are described and analyzed thoroughly.


10. “Finite Fields: Theory and Computation” by Shparlinski
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“Finite Fields: Theory and Computation” Book Review: This book systematically analyzes various computational and algorithmic problems in finite fields that have applications in computer science, coding theory, cryptography, numerical methods, etc. Polynomial factorization, finding irreducible and primitive polynomials, distribution of primitive polynomials and primitive points on elliptic curves, and construction of various types of bases are some of the problems discussed in great detail. The recent advances in the field of congruences are explained such as optimal coefficients, congruential pseudorandom number generators, modular arithmetic, etc. Primality testing, factoring integers, computation in algebraic number theory, etc. are some of the applications and developments of the computational number theory provided in this book.


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