Rational points on curves over finite fields :: theory and applications /
Discussion of theory and applications of algebraic curves over finite fields with many rational points.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
2001.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
285. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Discussion of theory and applications of algebraic curves over finite fields with many rational points. |
| Beschreibung: | 1 online resource (x, 245 pages) |
| Bibliographie: | Includes bibliographical references (pages 227-239) and index. |
| ISBN: | 9781107089297 1107089298 9781107325951 1107325951 9781107095540 1107095549 1299707203 9781299707207 |
Internformat
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| 100 | 1 | |a Niederreiter, Harald, |d 1944- |0 http://id.loc.gov/authorities/names/n83051156 | |
| 245 | 1 | 0 | |a Rational points on curves over finite fields : |b theory and applications / |c Harald Niederreiter, Chaoping Xing. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 2001. | ||
| 300 | |a 1 online resource (x, 245 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 285 | |
| 504 | |a Includes bibliographical references (pages 227-239) and index. | ||
| 505 | 0 | 0 | |t Background on Function Fields -- |t Riemann-Roch Theorem -- |t Divisor Class Groups and Ideal Class Groups -- |t Algebraic Extensions and the Hurwitz Formula -- |t Ramification Theory of Galois Extensions -- |t Constant Field Extensions -- |t Zeta Functions and Rational Places -- |t Class Field Theory -- |t Local Fields -- |t Newton Polygons -- |t Ramification Groups and Conductors -- |t Global Fields -- |t Ray Class Fields and Hilbert Class Fields -- |t Narrow Ray Class Fields -- |t Class Field Towers -- |t Explicit Function Fields -- |t Kummer and Artin-Schreier Extensions -- |t Cyclotomic Function Fields -- |t Drinfeld Modules of Rank 1 -- |t Function Fields with Many Rational Places -- |t Function Fields from Hilbert Class Fields -- |t Function Fields from Narrow Ray Class Fields -- |t The First Construction -- |t The Second Construction -- |t The Third Construction -- |t Function Fields from Cyclotomic Fields -- |t Explicit Function Fields -- |t Asymptotic Results -- |t Asymptotic Behavior of Towers -- |t The Lower Bound of Serre -- |t Further Lower Bounds for A(q[superscript m]) -- |t Explicit Towers -- |t Lower Bounds on A(2), A(3), and A(5) -- |t Applications to Algebraic Coding Theory -- |t Goppa's Algebraic-Geometry Codes -- |t Beating the Asymptotic Gilbert-Varshamov Bound -- |t NXL Codes -- |t XNL Codes -- |t A Propagation Rule for Linear Codes -- |t Applications to Cryptography -- |t Background on Stream Ciphers and Linear Complexity -- |t Constructions of Almost Perfect Sequences -- |t A Construction of Perfect Hash Families -- |t Hash Families and Authentication Schemes -- |t Applications to Low-Discrepancy Sequences. |
| 588 | 0 | |a Print version record. | |
| 520 | |a Discussion of theory and applications of algebraic curves over finite fields with many rational points. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Curves, Algebraic. |0 http://id.loc.gov/authorities/subjects/sh85034916 | |
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| 650 | 0 | |a Rational points (Geometry) |0 http://id.loc.gov/authorities/subjects/sh2001008362 | |
| 650 | 0 | |a Coding theory. |0 http://id.loc.gov/authorities/subjects/sh85027654 | |
| 650 | 6 | |a Courbes algébriques. | |
| 650 | 6 | |a Corps finis. | |
| 650 | 6 | |a Codage. | |
| 650 | 6 | |a Points rationnels (Géométrie) | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
| 650 | 7 | |a Coding theory |2 fast | |
| 650 | 7 | |a Curves, Algebraic |2 fast | |
| 650 | 7 | |a Finite fields (Algebra) |2 fast | |
| 650 | 7 | |a Rational points (Geometry) |2 fast | |
| 650 | 7 | |a Algebraische Kurve |2 gnd |0 http://d-nb.info/gnd/4001165-3 | |
| 650 | 7 | |a Algebraische Codierung |2 gnd |0 http://d-nb.info/gnd/4141834-7 | |
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| 776 | 0 | 8 | |i Print version: |a Niederreiter, Harald, 1944- |t Rational points on curves over finite fields. |d Cambridge ; New York : Cambridge University Press, 2001 |z 0521665434 |w (DLC) 2001025570 |w (OCoLC)46402143 |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn846496057 |
|---|---|
| _version_ | 1816882234202783744 |
| adam_text | |
| any_adam_object | |
| author | Niederreiter, Harald, 1944- |
| author2 | Xing, Chaoping, 1963- |
| author2_role | |
| author2_variant | c x cx |
| author_GND | http://id.loc.gov/authorities/names/n83051156 http://id.loc.gov/authorities/names/n99255842 |
| author_facet | Niederreiter, Harald, 1944- Xing, Chaoping, 1963- |
| author_role | |
| author_sort | Niederreiter, Harald, 1944- |
| author_variant | h n hn |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA565 |
| callnumber-raw | QA565 .N594 2001eb |
| callnumber-search | QA565 .N594 2001eb |
| callnumber-sort | QA 3565 N594 42001EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | 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 -- 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. |
| ctrlnum | (OCoLC)846496057 |
| 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 | ZDB-4-EBA-ocn846496057 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:22Z |
| institution | BVB |
| isbn | 9781107089297 1107089298 9781107325951 1107325951 9781107095540 1107095549 1299707203 9781299707207 |
| language | English |
| oclc_num | 846496057 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (x, 245 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Niederreiter, Harald, 1944- http://id.loc.gov/authorities/names/n83051156 Rational points on curves over finite fields : theory and applications / Harald Niederreiter, Chaoping Xing. Cambridge ; New York : Cambridge University Press, 2001. 1 online resource (x, 245 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 285 Includes bibliographical references (pages 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. Print version record. Discussion of theory and applications of algebraic curves over finite fields with many rational points. English. Curves, Algebraic. http://id.loc.gov/authorities/subjects/sh85034916 Finite fields (Algebra) http://id.loc.gov/authorities/subjects/sh85048351 Rational points (Geometry) http://id.loc.gov/authorities/subjects/sh2001008362 Coding theory. http://id.loc.gov/authorities/subjects/sh85027654 Courbes algébriques. Corps finis. Codage. Points rationnels (Géométrie) MATHEMATICS Geometry Algebraic. bisacsh Coding theory fast Curves, Algebraic fast Finite fields (Algebra) fast Rational points (Geometry) fast Algebraische Kurve gnd http://d-nb.info/gnd/4001165-3 Algebraische Codierung gnd http://d-nb.info/gnd/4141834-7 Galois-Feld gnd http://d-nb.info/gnd/4155896-0 Rationaler Punkt gnd http://d-nb.info/gnd/4177004-3 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 Xing, Chaoping, 1963- http://id.loc.gov/authorities/names/n99255842 Print version: Niederreiter, Harald, 1944- Rational points on curves over finite fields. Cambridge ; New York : Cambridge University Press, 2001 0521665434 (DLC) 2001025570 (OCoLC)46402143 London Mathematical Society lecture note series ; 285. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569249 Volltext |
| spellingShingle | Niederreiter, Harald, 1944- Rational points on curves over finite fields : theory and applications / London Mathematical Society lecture note series ; 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 -- 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. Curves, Algebraic. http://id.loc.gov/authorities/subjects/sh85034916 Finite fields (Algebra) http://id.loc.gov/authorities/subjects/sh85048351 Rational points (Geometry) http://id.loc.gov/authorities/subjects/sh2001008362 Coding theory. http://id.loc.gov/authorities/subjects/sh85027654 Courbes algébriques. Corps finis. Codage. Points rationnels (Géométrie) MATHEMATICS Geometry Algebraic. bisacsh Coding theory fast Curves, Algebraic fast Finite fields (Algebra) fast Rational points (Geometry) fast Algebraische Kurve gnd http://d-nb.info/gnd/4001165-3 Algebraische Codierung gnd http://d-nb.info/gnd/4141834-7 Galois-Feld gnd http://d-nb.info/gnd/4155896-0 Rationaler Punkt gnd http://d-nb.info/gnd/4177004-3 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 |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85034916 http://id.loc.gov/authorities/subjects/sh85048351 http://id.loc.gov/authorities/subjects/sh2001008362 http://id.loc.gov/authorities/subjects/sh85027654 http://d-nb.info/gnd/4001165-3 http://d-nb.info/gnd/4141834-7 http://d-nb.info/gnd/4155896-0 http://d-nb.info/gnd/4177004-3 |
| title | Rational points on curves over finite fields : theory and applications / |
| title_alt | 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 -- 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. |
| 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 | Curves, Algebraic. http://id.loc.gov/authorities/subjects/sh85034916 Finite fields (Algebra) http://id.loc.gov/authorities/subjects/sh85048351 Rational points (Geometry) http://id.loc.gov/authorities/subjects/sh2001008362 Coding theory. http://id.loc.gov/authorities/subjects/sh85027654 Courbes algébriques. Corps finis. Codage. Points rationnels (Géométrie) MATHEMATICS Geometry Algebraic. bisacsh Coding theory fast Curves, Algebraic fast Finite fields (Algebra) fast Rational points (Geometry) fast Algebraische Kurve gnd http://d-nb.info/gnd/4001165-3 Algebraische Codierung gnd http://d-nb.info/gnd/4141834-7 Galois-Feld gnd http://d-nb.info/gnd/4155896-0 Rationaler Punkt gnd http://d-nb.info/gnd/4177004-3 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 |
| topic_facet | Curves, Algebraic. Finite fields (Algebra) Rational points (Geometry) Coding theory. Courbes algébriques. Corps finis. Codage. Points rationnels (Géométrie) MATHEMATICS Geometry Algebraic. Coding theory Curves, Algebraic Algebraische Kurve Algebraische Codierung Galois-Feld Rationaler Punkt Eindige lichamen. Krommen. Corpos de classe. Teoria dos números. Criptologia. Computabilidade e complexidade. Champs modulaires. |
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| work_keys_str_mv | AT niederreiterharald rationalpointsoncurvesoverfinitefieldstheoryandapplications AT xingchaoping rationalpointsoncurvesoverfinitefieldstheoryandapplications |