## 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. |

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### 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 | |

### Common terms and phrases

Acad Acta Arith algebraic algorithm Amer BCH code binary Carlitz character of Fq character sums characteristic polynomial Chowla coefficients compute congruences considered Corollary cyclotomic polynomial defined Definition determined divides divisor Duke Math element of F equations equivalent Example exponential sums field F finite field follows formula function Gaussian sums given Golomb homogeneous linear recurring identity indeterminates irreducible factors irreducible polynomials Jacobi sums least period Lemma linear recurrence relation linear recurring sequence matrix minimal polynomial modulo monic monic irreducible polynomials multiplicative character nomial nonzero number of solutions Number Theory obtain orthogonal permutation polynomial polynomial of Fq polynomial over Fq polynomials in Fq[x positive integer primitive element primitive polynomial Proc proof of Theorem Prove quadratic character quadratic form reine angew residue class result ring root of unity Russian sequence in Fq splitting field subfield trivial Univ vector space