Algebraic Function Fields and Codes

• Main Author: Stichtenoth, Henning. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Graduate Texts in Mathematics, 254
• Subjects: Mathematics.; Data structures (Computer science).; Algebra.; Geometry, algebraic.; Engineering mathematics.; Algebraic Geometry.; Data Structures, Cryptology and Information Theory.; Information and Communication, Circuits.; Appl.Mathematics/Computational Methods of Engineering.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-76878-4

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 an...

Table of Contents:

• 1. Foundations of the Theory of Algebraic Function Fiels
• 2. Algebraic Geometry 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. Asymptotic Bounds for the Number of Rational Places
• 8. More about Algebraic Geometry Codes
• 9. Subfield Subcodes and Trace Codes
• Appendix A. Field Theory
• Appendix B. Algebraic Curves and Algebraic Function Fields
• Bibliography
• List of Notations
• Index.