Algebraic Function Fields and Codes

• Main Author: Stichtenoth, Henning (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Graduate Texts in Mathematics, 254
• Subjects: Mathematics.; Data structures (Computer science).; Algebra.; Algebraic geometry.; Information theory.; Applied mathematics.; Engineering mathematics.; Algebraic Geometry.; Data Structures, Cryptology and Information Theory.; Information and Communication, Circuits.; Appl.Mathematics/Computational Methods of Engineering.

 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. Other exercises 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. 

 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.