Degeneration of Shimura surfaces and a problem in coding theory
FCT '85 Fundamentals of Computation Theory
Excellent codes from modular curves
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
New Optimal Tame Towers of Function Fields over Small Finite Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Recursive towers of function fields over finite fields
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Towards a classification of recursive towers of function fields over finite fields
Finite Fields and Their Applications
Finite Fields and Their Applications
On a Problem of Garcia, Stichtenoth, and Thomas
Finite Fields and Their Applications
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For a towerF"1@?F"2@? ... of algebraic function fieldsF"i/F"q, define @l = lim"i"-"~N(F"i)/g(F"i), whereN(F"i) is the number of rational places andg(F"i) is the genus ofF"i/F"q. The tower is said to be asymptotically good if @l 0. We give a very simple explicit example of an asymptotically good tower for all non-prime fields F"q. In this example, all stepsF"i"+"1/F"iare tamely ramified Kummer extensions. We then show that any function fieldF/F"qhaving at least one rational place can be embedded into an asymptotically good tower, and we study the behaviour of @l in the compositum of a towerF"1@?F"2@? ... with an extensionE/F"1.