Finite fields:
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 circuits. This book is devoted entirely to the theory of finite fields, and it provides comprehensive...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1997
|
| Edition: | 2. ed. |
| Series: | Encyclopedia of mathematics and its applications
20 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | 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 circuits. 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. |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XIV, 755 S. graph. Darst. |
| ISBN: | 0521392314 0521065674 9780521392310 9780521065672 |
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MARC
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Record in the Search Index
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Titel: Finite fields
Autor: Lidl, Rudolf
Jahr: 1997
Contents Foreword .xi Preface .xiii Chapter 1 Algebraic Foundations.1 1 Groups.2 2 Rings and Fields .11 3 Polynomials.18 4 Field Extensions.30 Notes .37 Exercises.40 Chapter 2 Structure of Finite Fields.47 1 Characterization of Finite Fields .48 2 Roots of Irreducible Polynomials.51 3 Traces, Norms, and Bases.54 4 Roots of Unity and Cyclotomie Polynomials.63 vii
Contents viii 5 Representation of Elements of Finite Fields.66 6 Wedderbum’s Theorem.69 Notes .73 Exercises.78 Chapter 3 Polynomials over Finite Fields.83 1 Order of Polynomials and Primitive Polynomials.84 2 Irreducible Polynomials.91 3 Construction of Irreducible Polynomials.96 4 Linearized Polynomials.107 5 Binomials and Trinomials.124 Notes .131 Exercises.140 Chapter 4 Factorization of Polynomials.147 1 Factorization over Small Finite Fields.148 2 Factorization over Large Finite Fields.157 3 Calculation of Roots of Polynomials.168 Notes .177 Exercises.183 Chapter 5 Exponential Sums.186 1 Characters.187 2 Gaussian Sums.192 3 Jacobi Sums.205 4 Character Sums with Polynomial Arguments.217 5 Further Results on Character Sums.226 Notes .240 Exercises.257 Chapter 6 Equations over Finite Fields.268 1 Elementary Results on the Number of Solutions.269 2 Quadratic Forms.278 3 Diagonal Equations.289 4 The Stepanov-Schmidt Method.300 Notes .317 Exercises.339 Chapter 7 Permutation Polynomials.347 1 Criteria for Permutation Polynomials.348 2 Special Types of Permutation
Polynomials.351
Contents IX 3 Groups of Permutation Polynomials.357 4 Exceptional Polynomials.362 5 Permutation Polynomials in Several Indeterminates.368 Notes .377 Exercises.389 Chapter 8 Linear Recurring Sequences.394 1 Feedback Shift Registers, Periodicity Properties.395 2 Impulse Response Sequences, Characteristic Polynomial .402 3 Generating Functions.411 4 The Minimal Polynomial.418 5 Families of Linear Recurring Sequences .423 6 Characterization of Linear Recurring Sequences.437 7 Distribution Properties of Linear Recurring Sequences . . . 444 Notes .453 Exercises.464 Chapter 9 Applications of Finite Fields.470 1 Linear Codes. 471 2 Cyclic Codes .482 3 Finite Geometries.496 4 Combinatorics.508 5 Linear Modular Systems.517 Notes .528 Exercises. 533 Chapter 10 Tables.541 1 Computation in Finite Fields.541 2 Tables of Irreducible Polynomials.543 Notes .544 Tables.546 Bibliography.567 List of Symbols.727 Author Index.731 Subject Index.747 |
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| edition | 2. ed. |
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| illustrated | Illustrated |
| indexdate | 2024-07-20T07:51:31Z |
| institution | BVB |
| isbn | 0521392314 0521065674 9780521392310 9780521065672 |
| language | English |
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| publishDate | 1997 |
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| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Lidl, Rudolf 1948- Verfasser (DE-588)136240755 aut Finite fields Rudolf Lidl ; Harald Niederreiter 2. ed. Cambridge [u.a.] Cambridge Univ. Press 1997 XIV, 755 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 20 Hier auch später erschienene, unveränderte Nachdrucke 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 circuits. 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. Galois-Feld Computerwiskunde gtt Corps finis Eindige lichamen gtt Finite fields (Algebra) Galois-Feld (DE-588)4155896-0 gnd rswk-swf Galois-Feld (DE-588)4155896-0 s DE-604 Niederreiter, Harald 1944- Verfasser (DE-588)117716979 aut Encyclopedia of mathematics and its applications 20 (DE-604)BV000903719 20 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007667135&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lidl, Rudolf 1948- Niederreiter, Harald 1944- Finite fields Encyclopedia of mathematics and its applications Galois-Feld Computerwiskunde gtt Corps finis Eindige lichamen gtt Finite fields (Algebra) Galois-Feld (DE-588)4155896-0 gnd |
| subject_GND | (DE-588)4155896-0 |
| title | Finite fields |
| title_auth | Finite fields |
| title_exact_search | Finite fields |
| title_full | Finite fields Rudolf Lidl ; Harald Niederreiter |
| title_fullStr | Finite fields Rudolf Lidl ; Harald Niederreiter |
| title_full_unstemmed | Finite fields Rudolf Lidl ; Harald Niederreiter |
| title_short | Finite fields |
| title_sort | finite fields |
| topic | Galois-Feld Computerwiskunde gtt Corps finis Eindige lichamen gtt Finite fields (Algebra) Galois-Feld (DE-588)4155896-0 gnd |
| topic_facet | Galois-Feld Computerwiskunde Corps finis Eindige lichamen Finite fields (Algebra) |
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