Curves with Many Points and Their Applications
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On Representations of Algebraic-Geometric Codes for List Decoding
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
Asymmetric Code-Theoretical Schemes Constructed with the Use of Algebraic Geometric Codes
Cybernetics and Systems Analysis
On maximal curves with Frobenius dimension 3
Designs, Codes and Cryptography
On some open problems on maximal curves
Designs, Codes and Cryptography
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Algebraic function fields (or equivalently, algebraic curves) provide a useful tool for coding theory (for instance, algebraic-geometric codes and trace codes), but also for other branches of information theory. In these applications, the number of rational places of a function field plays a crucial role. One is particularly interested in function fields having a large number of rational places. After a short introduction into the mathematical theory of algebraic functions, the paper gives a survey of old and new results on the number of rational places of function fields