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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.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2001.
|
| Colección: | London Mathematical Society lecture note series ;
285. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.