Finite Fields, Volume 20, Part 1The theory of finite fields is a branch of algebra that has come to the fore becasue 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. Workd out examples and lists of exercises found throughout the book make it useful as a text for advanced level courses. |
Contents
Structure of Finite Fields | 47 |
Polynomials over Finite Fields | 83 |
Factorization of Polynomials | 147 |
Exponential Sums | 186 |
Equations over Finite Fields | 268 |
Permutation Polynomials | 347 |
Linear Recurring Sequences | 394 |
Applications of Finite Fields | 470 |
Tables | 541 |
Bibliography | 567 |
List of Symbols | 727 |
| 747 | |
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Common terms and phrases
a₁ Acta Arith additive character algebraic algorithm Amer c₁ Carlitz character of F character sums characteristic polynomial Chowla coefficients compute congruences cyclic cyclotomic cyclotomic polynomial d₁ defined deg(f determined divides divisor Duke Math elements of F equations exponential sums F₁ F₂ field F finite field follows formula function Gaussian sums homogeneous linear recurring identity indeterminates irreducible polynomials Jacobi sums Kloosterman sums least period Lemma Let f linear recurrence relation linear recurring sequence matrix minimal polynomial modulo monic monic irreducible polynomials multiplicative character nomial nontrivial nonzero number of solutions Number Theory obtain permutation polynomial polynomial f polynomial of F polynomial over F polynomials in F,[x positive integer primitive element primitive polynomial Proc Prove q-polynomial quadratic character quadratic form reine angew result ring Russian S₁ sequence in F splitting field vector space x₁