Topics in Geometry, coding theory and cryptography

Includes index.

Includes bibliographical references

1 Explicit towers of function fields over finite fields / by A. Garcia and H. Stichtenoth
2 Function fields over finite fields and their applications to cryptography / by H. Niederreiter, H. Wang, and C. Xing
3 Artin-Schreier extensions and their applications / by C. Güneri and F. Özbudak
4 Pseudorandom sequences / by A. Topuzoğlu and A. Winterhof
5 Group structure of elliptic curves over finite fields and applications / by R. Murty and I. Shparlinski

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.