Algebraic function fields and codes
Author(s)
Bibliographic Information
Algebraic function fields and codes
（Universitext）
Springer-Verlag, c1993
- : gw
- : us
Available at / 83 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
: Berlindc20:512/st512070264944
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Note
Bibliography: p. [251]-252
Includes list of notation and index
Description and Table of Contents
Description
This book has two objectives. The first is to fill a void in the existing mathematical literature by providing a modern, self-contained and in-depth exposition of the theory of algebraic function fields. The topics include the Riemann-Roch theorem, algebraic extensions of function fields, ramifications theory and differentials. Particular emphasis is placed on function fields over a finite constant field, leading into zeta functions and the Hasse-Weil theorem. Numerous examples illustrate the general theory. Error-correcting codes are in widespread use for the reliable transmission of information. Perhaps the most fascinating of all the ties that link the theory of these codes to mathematics is the construction by V.D. Goppa, of powerful codes using techniques borrowed from algebraic geometry. Algebraic function fields provide the most elementary approach to Goppa's ideas, and the second objective of this book is to provide an introduction to Goppa's algebraic-geometric codes along these lines. The codes, their parameters and links with traditional codes such as classical Goppa, Peed-Solomon and BCH codes are treated at an early stage of the book.
Subsequent chapters include a decoding algorithm for these codes as well as a discussion of their subfield subcodes and trace codes. Stichtenoth's book will be very useful to students and researchers in algebraic geometry and coding theory and to computer scientists and engineers interested in information transmission.
Table of Contents
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
by "Nielsen BookData"