Finite Fields, Nide 20,Osa 1Cambridge University Press, 1997 - 755 sivua The 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. |
Sisältö
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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a₁ Acad Acta Arith additive character algebraic algorithm Amer b₁ c₁ Carlitz character of F character sums characteristic polynomial Chowla coefficients compute congruences cyclic cyclotomic cyclotomic polynomial defined Definition deg(ƒ determined divides divisor Duke Math element of F equations exponential sums F₂ field F finite field follows formula function Gaussian sums given homogeneous linear recurring identity indeterminates irreducible polynomials Jacobi 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 ƒ polynomial of F polynomial over F positive integer prime fields primitive element primitive polynomial Proc Prove q-polynomial quadratic character quadratic form reine angew residue class result ring Russian S₁ sequence in F splitting field ß³ vector space