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This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.…mehr

Produktbeschreibung
This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.


Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

  • Produktdetails
  • Verlag: Springer-Verlag GmbH
  • Seitenzahl: 360
  • Erscheinungstermin: 11. Februar 2009
  • Englisch
  • ISBN-13: 9783540768784
  • Artikelnr.: 37368000
Inhaltsangabe
Foundations of the Theory of Algebraic Function Fields.- Algebraic Geometry Codes.- Extensions of Algebraic Function Fields.- Differentials of Algebraic Function Fields.- Algebraic Function Fields over Finite Constant Fields.- Examples of Algebraic Function Fields.- Asymptotic Bounds for the Number of Rational Places.- More about Algebraic Geometry Codes.- Subfield Subcodes and Trace Codes.

1. Foundations of the Theory of Algebraic Function Fiels
- 2. Geometric Goppa Codes
- 3. Extensions of Algebraic Function Fields
- 4. Differentials of Algebraic Function Fields
- 5. Algebraic Function Fields over Finite Constant Fields
- 6. Examples of Algebraic Function Fields
- 7. More about Geometric Goppy Codes
- 8. Subfield Subcodes and Trace Codes
- Appendix A. Field Theory
- Appendix B. Algebraic Curves and Algebraic Function Fields
- Bibliography
- List of Notations
- Index
Rezensionen
From the reviews of the second edition: "In this book we have an exposition of the theory of function fields in one variable from the algebraic point of view ... . The book is carefully written, the concepts are well motivated and plenty of examples help to understand the ideas and proofs and so it can be used as a textbook for an introductory course on the (classical) arithmetic of function fields with an application to coding theory." (Felipe Zaldivar, MAA Online, January, 2009)