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. 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.
Author(s): Arnaldo Garcia (Editor), Henning Stichtenoth (Editor)
Series: Algebra and Applications
Edition: 1
Publisher: Springer
Year: 2007
Language: English
Pages: 211
Contents......Page 6
Foreword......Page 8
1 Introduction......Page 12
2 Towers and Codes......Page 16
3 Genus and Splitting Rate of a Tower......Page 27
4 Explicit Tame Towers......Page 35
5 Explicit Wild Towers......Page 42
6 Miscellaneous Results......Page 58
References......Page 66
1 Introduction......Page 70
2 Applications to Combinatorial Cryptography......Page 71
3 Applications to Stream Ciphers and Linear Complexity......Page 100
References......Page 110
1 Introduction......Page 116
2 Artin-Schreier Extensions......Page 118
3 Cyclic Codes and Their Weights......Page 122
4 Trace Codes......Page 131
5 Maximal Function Fields......Page 137
References......Page 141
1 Introduction......Page 145
2 Linear Complexity and Linear Complexity Profile......Page 147
3 Autocorrelation and Related Distribution Measures for Binary Sequences......Page 164
4 Discrepancy and Uniform Distribution......Page 167
References......Page 172
1 Introduction......Page 177
2 Group Structure......Page 181
3 Applications to Cryptography......Page 190
References......Page 197
Appendix: Algebraic Function Fields......Page 205
About the Authors......Page 209
