On the Construction of Galois Towers

In this paper we study an asymptotically optimal tame tower over the field with p(2) elements introduced by Garcia-Stichtenoth. This tower is related with a modular tower, for which explicit equations were given by Elkies. We use this relation to investigate its Galois closure. Along the way, we obtain information about the structure of the Galois closure of X-0(p(n)) over X-0(p(r)), for integers 1 < r < n and prime p and the Galois closure of other modular towers (X-0(p(n)))n.


Published in:
Arithmetic, Geometry, Cryptography And Coding Theory, 487, 9-20
Presented at:
11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory, Marseilles, FRANCE, Nov 05-09, 2007
Year:
2009
Publisher:
American Mathematical Society, P.O. Box 6248 Ms. Phoebe Murdock, Providence, Ri 02940 Usa
Keywords:
Laboratories:




 Record created 2010-11-30, last modified 2018-03-17


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