The theory of algebraic function fields has its origins in number theory, complex analysis (compact Riemann surfaces), and algebraic geometry. Since about 1980, function fields have found surprising applications in other branches of mathematics such as coding theory, cryptography, sphere packings and others. The main objective of this book is to provide a purely algebraic, self-contained and in-depth exposition of the theory of function fields. This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded. Moreover, the present edition contains numerous exercises. Some of them are fairly easy and help the reader to understand the basic material. Otherexercises are more advanced and cover additional material which could not be included in the text. This volume is mainly addressed to graduate students in mathematics and theoretical computer science, cryptography, coding theory and electrical engineering. Well-established popular textbook INDICE: 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.
- ISBN: 978-3-540-76877-7
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 365
- Fecha Publicación: 01/12/2008
- Nº Volúmenes: 1
- Idioma: Inglés
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- MATEMÁTICAS /
- ÁLGEBRA