| Description |
1 online resource (x, 245 pages). |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
London Mathematical Society lecture note series ; 285
|
|
London Mathematical Society lecture note series ; 285.
|
| Bibliography |
Includes bibliographical references (pages 227-239) and index. |
| 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 -- First Construction -- Second Construction -- Third Construction -- Function Fields from Cyclotomic Fields -- Explicit Function Fields -- Asymptotic Results -- Asymptotic Behavior of Towers -- 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. |
| Summary |
Discussion of theory and applications of algebraic curves over finite fields with many rational points. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Curves, Algebraic.
|
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Curves, Algebraic. |
|
Finite fields (Algebra)
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Finite fields (Algebra) |
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Rational points (Geometry)
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Rational points (Geometry) |
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Coding theory.
|
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Coding theory. |
| Genre/Form |
Electronic books.
|
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Electronic books.
|
| Added Author |
Xing, Chaoping, 1963-
|
| Other Form: |
Print version: Niederreiter, Harald, 1944- Rational points on curves over finite fields. Cambridge ; New York : Cambridge University Press, 2001 0521665434 (DLC) 2001025570 (OCoLC)46402143 |
| ISBN |
9781107089297 (electronic book) |
|
1107089298 (electronic book) |
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9781107325951 (electronic book) |
|
1107325951 (electronic book) |
|
9781107095540 |
|
1107095549 |
|
0521665434 |
|
9780521665438 |
|
