Rational points on curves over finite fields : theory and applications /
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| Author / Creator: | Niederreiter, Harald, 1944- |
|---|---|
| Imprint: | Cambridge ; New York : Cambridge University Press, 2001. |
| Description: | 1 online resource (x, 245 pages) |
| Language: | English |
| Series: | London Mathematical Society lecture note series ; 285 London Mathematical Society lecture note series ; 285. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11189513 |
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| 050 | 4 | |a QA565 |b .N594 2001eb | |
| 072 | 7 | |a MAT |x 012010 |2 bisacsh | |
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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 | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 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 | |
| 650 | 0 | |a Finite fields (Algebra) |0 http://id.loc.gov/authorities/subjects/sh85048351 | |
| 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 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
| 650 | 7 | |a Coding theory. |2 fast |0 (OCoLC)fst00866237 | |
| 650 | 7 | |a Curves, Algebraic. |2 fast |0 (OCoLC)fst00885451 | |
| 650 | 7 | |a Finite fields (Algebra) |2 fast |0 (OCoLC)fst00924905 | |
| 650 | 7 | |a Rational points (Geometry) |2 fast |0 (OCoLC)fst01090266 | |
| 650 | 1 | 7 | |a Eindige lichamen. |2 gtt |
| 650 | 1 | 7 | |a Krommen. |2 gtt |
| 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 | |
| 650 | 7 | |a Galois-Feld |2 gnd |0 http://d-nb.info/gnd/4155896-0 | |
| 650 | 7 | |a Rationaler Punkt |2 gnd |0 http://d-nb.info/gnd/4177004-3 | |
| 650 | 7 | |a Corpos de classe. |2 larpcal | |
| 650 | 7 | |a Teoria dos números. |2 larpcal | |
| 650 | 7 | |a Criptologia. |2 larpcal | |
| 650 | 7 | |a Computabilidade e complexidade. |2 larpcal | |
| 650 | 7 | |a Courbes algébriques. |2 ram | |
| 650 | 7 | |a Champs modulaires. |2 ram | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Xing, Chaoping, |d 1963- |0 http://id.loc.gov/authorities/names/n99255842 | |
| 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 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 285. |0 http://id.loc.gov/authorities/names/n42015587 | |
| 903 | |a HeVa | ||
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| 928 | |t Library of Congress classification |a QA565 .N594 2001eb |l Online |c UC-FullText |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=569249 |z eBooks on EBSCOhost |g ebooks |i 12390384 | ||