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15 years after the ?rst printing of Algebraic Function Fields and Codes, the mathematics editors of Springer Verlag encouraged me to revise and extend the book. Besides numerous minor corrections and amendments, the second edition di?ers from the ?rst one in two respects. Firstly I have included a series of exercises at the end of each chapter. Some of these exercises are fairly easy and should help the reader to understand the basic concepts, others are more advanced and cover additional material. Secondly a new chapter titled "Asymptotic Bounds for the Number of Rational Places" has been...

15 years after the ?rst printing of Algebraic Function Fields and Codes, the mathematics editors of Springer Verlag encouraged me to revise and extend the book. Besides numerous minor corrections and amendments, the second edition di?ers from the ?rst one in two respects. Firstly I have included a series of exercises at the end of each chapter. Some of these exercises are fairly easy and should help the reader to understand the basic concepts, others are more advanced and cover additional material. Secondly a new chapter titled "Asymptotic Bounds for the Number of Rational Places" has been...

The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppas discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.

The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppas discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.

About ten years ago, V.D. Goppa found a surprisingconnection between the theory of algebraic curves over afinite field and error-correcting codes. The aim of themeeting "Algebraic Geometry and Coding Theory" was to give asurvey on the present state of research in this field andrelated topics. The proceedings contain research papers onseveral aspects of the theory, among them: Codes constructedfrom special curves and from higher-dimensional varieties, Decoding of algebraic geometric codes, Trace codes, Exponen-tial sums, Fast multiplication in finite fields, Asymptoticnumber of points on...

Thisvolumerepresentstherefereedproceedingsofthe7thInternationalC- ference on Finite Fields and Applications (F 7) held during May 5 9, q 2003, in Toulouse, France. The conference was hosted by the Pierre Baudis C- gress Center, downtown, and held at the excellent conference facility. This event continued a series of biennial international conferences on Finite Fields and - plications, following earlier meetings at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University of Glasgow (UK) in July 1995, the University of Waterloo (Canada) in August 1997, the...