Topics in Geometry, Coding Theory and Cryptography

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.

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.)