Overview
- Serves as an introduction and invitation to several main directions of research in the area of Function Fields over Finite Fields and their various applications to Information Theory
- Reasonably accessible (by a friendly presentation of topics) to interested researchers and even to students and nonspecialists
- The diversity of the themes in this volume is unique in the literature
- Recent topics which are not treated in other books or survey articles
- Algebraic function fields provide a tool which often gives better results than traditional methods in many applications (coding theory, cryptography, sequence design, etc.)
Part of the book series: Algebra and Applications (AA, volume 6)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (5 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory, such as coding theory, sphere packings and lattices, sequence design, and cryptography. The use of function fields often led to better results than those of classical approaches.
This book presents survey articles on some of these new developments. Most of the material is directly related to the interaction between function fields and their various applications; in particular the structure and the number of rational places of function fields are of great significance. The topics focus on material which has not yet been presented in other books or survey articles. Wherever applications are pointed out, a special effort has been made to present some background concerning their use.
Reviews
From the reviews:
"This book contains five surveys on different topic related to coding theory. The chapters are largely independent from each other and one can browse freely through them. ... The book is well-written and I think it may be valuable both for researchers and for students with background in algebra. ... In fact, the main interest of this book is that it focuses on topics not covered in other books on coding theory." (Fabio Mainardi, MAA Online, January, 2007)
Editors and Affiliations
Bibliographic Information
Book Title: Topics in Geometry, Coding Theory and Cryptography
Editors: Arnaldo Garcia, Henning Stichtenoth
Series Title: Algebra and Applications
DOI: https://doi.org/10.1007/1-4020-5334-4
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media B.V. 2007
Hardcover ISBN: 978-1-4020-5333-7Published: 18 October 2006
Softcover ISBN: 978-90-481-7345-7Published: 30 November 2010
eBook ISBN: 978-1-4020-5334-4Published: 15 November 2006
Series ISSN: 1572-5553
Series E-ISSN: 2192-2950
Edition Number: 1
Number of Pages: X, 201
Topics: Number Theory, Algebraic Geometry, Coding and Information Theory, Cryptology