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Algebra --- Algebra, Abstract. --- Algèbre abstraite --- Mathematics --- Physical Sciences & Mathematics --- Algebra, Abstract --- Lattice theory --- Semigroups --- Cryptography --- Coding theory --- Treillis, Théorie des --- Semigroupes --- Cryptographie --- Codage --- Algèbre abstraite --- Cryptography. --- Algèbre abstraite. --- Treillis, Théorie des. --- Semigroupes. --- Cryptographie. --- Codage. --- Algebra. --- Mathematical analysis --- Abstract algebra --- Algebra, Universal --- Logic, Symbolic and mathematical --- Set theory

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Finite fields (Algebra) --- Corps finis --- 512.62 --- 519.1 --- #KVIV:BB --- #KOPO:Prof. R. Holvoet --- 519.72 --- Modular fields (Algebra) --- Algebra, Abstract --- Algebraic fields --- Galois theory --- Modules (Algebra) --- Fields. Polynomials --- Combinatorics. Graph theory --- Information theory: mathematical aspects --- Finite fields (Algebra). --- 519.72 Information theory: mathematical aspects --- 519.1 Combinatorics. Graph theory --- 512.62 Fields. Polynomials

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The theory of finite fields is a branch of algebra that has come to the fore because of its diverse applications in such areas as combinatorics, coding theory and the mathematical study of switching ciruits. This book is devoted entirely to the theory of finite fields, and it provides comprehensive coverage of the literature. Bibliographical notes at the end of each chapter give an historical survey of the development of the subject. Worked-out examples and lists of exercises found throughout the book make it useful as a text for advanced-level courses.

Finite fields (Algebra) --- Modules (Algebra) --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- Modular fields (Algebra) --- Algebra, Abstract --- Algebraic fields --- Galois theory --- Finite fields (Algebra).

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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 updated edition 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. It will appeal to advanced undergraduates and graduate students taking courses on topics in algebra, whether they have backgrounds in mathematics, electrical engineering or computer science. Non-specialists will also find this a readily accessible introduction to an active and increasingly important subject.

Finite fields (Algebra)