Rational points on curves over finite fields: theory and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2001
|
| Schriftenreihe: | London Mathematical Society lecture note series
285 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 227-239) and index Background on Function Fields -- - Riemann-Roch Theorem -- - Divisor Class Groups and Ideal Class Groups -- - Algebraic Extensions and the Hurwitz Formula -- - Ramification Theory of Galois Extensions -- - Constant Field Extensions -- - Zeta Functions and Rational Places -- - Class Field Theory -- - Local Fields -- - Newton Polygons -- - Ramification Groups and Conductors -- - Global Fields -- - Ray Class Fields and Hilbert Class Fields -- - Narrow Ray Class Fields -- - Class Field Towers -- - Explicit Function Fields -- - Kummer and Artin-Schreier Extensions -- - Cyclotomic Function Fields -- - Drinfeld Modules of Rank 1 -- - Function Fields with Many Rational Places -- - Function Fields from Hilbert Class Fields -- - Function Fields from Narrow Ray Class Fields -- - The First Construction -- - The Second Construction -- - The Third Construction -- - Function Fields from Cyclotomic Fields -- - Explicit Function Fields -- - Asymptotic Results -- - Asymptotic Behavior of Towers -- - The Lower Bound of Serre -- - Further Lower Bounds for A(q[superscript m]) -- - Explicit Towers -- - Lower Bounds on A(2), A(3), and A(5) -- - Applications to Algebraic Coding Theory -- - Goppa's Algebraic-Geometry Codes -- - Beating the Asymptotic Gilbert-Varshamov Bound -- - NXL Codes -- - XNL Codes -- - A Propagation Rule for Linear Codes -- - Applications to Cryptography -- - Background on Stream Ciphers and Linear Complexity -- - Constructions of Almost Perfect Sequences -- - A Construction of Perfect Hash Families -- - Hash Families and Authentication Schemes -- - Applications to Low-Discrepancy Sequences |
| Beschreibung: | 1 Online-Ressource (x, 245 p.) |
| ISBN: | 0521665434 1107089298 1107325951 9780521665438 9781107089297 9781107325951 |
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Datensatz im Suchindex
| _version_ | 1804175530707124224 |
|---|---|
| any_adam_object | |
| author | Niederreiter, Harald |
| author_facet | Niederreiter, Harald |
| author_role | aut |
| author_sort | Niederreiter, Harald |
| author_variant | h n hn |
| building | Verbundindex |
| bvnumber | BV043110955 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)846496057 (DE-599)BVBBV043110955 |
| dewey-full | 516.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/52 |
| dewey-search | 516.3/52 |
| dewey-sort | 3516.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043110955 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:45Z |
| institution | BVB |
| isbn | 0521665434 1107089298 1107325951 9780521665438 9781107089297 9781107325951 |
| language | English |
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| publishDate | 2001 |
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| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Niederreiter, Harald Verfasser aut Rational points on curves over finite fields theory and applications Harald Niederreiter, Chaoping Xing Cambridge Cambridge University Press 2001 1 Online-Ressource (x, 245 p.) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 285 Includes bibliographical references (p. 227-239) and index Background on Function Fields -- - Riemann-Roch Theorem -- - Divisor Class Groups and Ideal Class Groups -- - Algebraic Extensions and the Hurwitz Formula -- - Ramification Theory of Galois Extensions -- - Constant Field Extensions -- - Zeta Functions and Rational Places -- - Class Field Theory -- - Local Fields -- - Newton Polygons -- - Ramification Groups and Conductors -- - Global Fields -- - Ray Class Fields and Hilbert Class Fields -- - Narrow Ray Class Fields -- - Class Field Towers -- - Explicit Function Fields -- - Kummer and Artin-Schreier Extensions -- - Cyclotomic Function Fields -- - Drinfeld Modules of Rank 1 -- - Function Fields with Many Rational Places -- - Function Fields from Hilbert Class Fields -- - Function Fields from Narrow Ray Class Fields -- - The First Construction -- - The Second Construction -- - The Third Construction -- - Function Fields from Cyclotomic Fields -- - Explicit Function Fields -- - Asymptotic Results -- - Asymptotic Behavior of Towers -- - The Lower Bound of Serre -- - Further Lower Bounds for A(q[superscript m]) -- - Explicit Towers -- - Lower Bounds on A(2), A(3), and A(5) -- - Applications to Algebraic Coding Theory -- - Goppa's Algebraic-Geometry Codes -- - Beating the Asymptotic Gilbert-Varshamov Bound -- - NXL Codes -- - XNL Codes -- - A Propagation Rule for Linear Codes -- - Applications to Cryptography -- - Background on Stream Ciphers and Linear Complexity -- - Constructions of Almost Perfect Sequences -- - A Construction of Perfect Hash Families -- - Hash Families and Authentication Schemes -- - Applications to Low-Discrepancy Sequences Courbes algébriques Corps finis Codage Eindige lichamen gtt Krommen gtt Corpos de classe larpcal Teoria dos números larpcal Criptologia larpcal Computabilidade e complexidade larpcal Courbes algébriques ram Champs modulaires ram MATHEMATICS / Geometry / Algebraic bisacsh Coding theory fast Curves, Algebraic fast Finite fields (Algebra) fast Rational points (Geometry) fast Curves, Algebraic Finite fields (Algebra) Rational points (Geometry) Coding theory Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Feld Mathematik (DE-588)4280861-3 gnd rswk-swf Galois-Feld (DE-588)4155896-0 gnd rswk-swf Rationaler Punkt (DE-588)4177004-3 gnd rswk-swf Algebraische Codierung (DE-588)4141834-7 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 s Galois-Feld (DE-588)4155896-0 s Rationaler Punkt (DE-588)4177004-3 s Algebraische Codierung (DE-588)4141834-7 s 1\p DE-604 Feld Mathematik (DE-588)4280861-3 s 2\p DE-604 Xing, Chaoping Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=569249 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Niederreiter, Harald Rational points on curves over finite fields theory and applications Courbes algébriques Corps finis Codage Eindige lichamen gtt Krommen gtt Corpos de classe larpcal Teoria dos números larpcal Criptologia larpcal Computabilidade e complexidade larpcal Courbes algébriques ram Champs modulaires ram MATHEMATICS / Geometry / Algebraic bisacsh Coding theory fast Curves, Algebraic fast Finite fields (Algebra) fast Rational points (Geometry) fast Curves, Algebraic Finite fields (Algebra) Rational points (Geometry) Coding theory Algebraische Kurve (DE-588)4001165-3 gnd Feld Mathematik (DE-588)4280861-3 gnd Galois-Feld (DE-588)4155896-0 gnd Rationaler Punkt (DE-588)4177004-3 gnd Algebraische Codierung (DE-588)4141834-7 gnd |
| subject_GND | (DE-588)4001165-3 (DE-588)4280861-3 (DE-588)4155896-0 (DE-588)4177004-3 (DE-588)4141834-7 |
| title | Rational points on curves over finite fields theory and applications |
| title_auth | Rational points on curves over finite fields theory and applications |
| title_exact_search | Rational points on curves over finite fields theory and applications |
| title_full | Rational points on curves over finite fields theory and applications Harald Niederreiter, Chaoping Xing |
| title_fullStr | Rational points on curves over finite fields theory and applications Harald Niederreiter, Chaoping Xing |
| title_full_unstemmed | Rational points on curves over finite fields theory and applications Harald Niederreiter, Chaoping Xing |
| title_short | Rational points on curves over finite fields |
| title_sort | rational points on curves over finite fields theory and applications |
| title_sub | theory and applications |
| topic | Courbes algébriques Corps finis Codage Eindige lichamen gtt Krommen gtt Corpos de classe larpcal Teoria dos números larpcal Criptologia larpcal Computabilidade e complexidade larpcal Courbes algébriques ram Champs modulaires ram MATHEMATICS / Geometry / Algebraic bisacsh Coding theory fast Curves, Algebraic fast Finite fields (Algebra) fast Rational points (Geometry) fast Curves, Algebraic Finite fields (Algebra) Rational points (Geometry) Coding theory Algebraische Kurve (DE-588)4001165-3 gnd Feld Mathematik (DE-588)4280861-3 gnd Galois-Feld (DE-588)4155896-0 gnd Rationaler Punkt (DE-588)4177004-3 gnd Algebraische Codierung (DE-588)4141834-7 gnd |
| topic_facet | Courbes algébriques Corps finis Codage Eindige lichamen Krommen Corpos de classe Teoria dos números Criptologia Computabilidade e complexidade Champs modulaires MATHEMATICS / Geometry / Algebraic Coding theory Curves, Algebraic Finite fields (Algebra) Rational points (Geometry) Algebraische Kurve Feld Mathematik Galois-Feld Rationaler Punkt Algebraische Codierung |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=569249 |
| work_keys_str_mv | AT niederreiterharald rationalpointsoncurvesoverfinitefieldstheoryandapplications AT xingchaoping rationalpointsoncurvesoverfinitefieldstheoryandapplications |