New optimal tame towers of function fields over small finite fields

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2369, Issue , 2002, Pages 372-389

  Li, Wen Ching W ^a   Maharaj, Hiren ^b   Stichtenoth, Henning ^c   Elkies, Noam D ^d  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b CLEMSON UNIVERSITY   (United States)

^c UNIVERSITY OF DUISBURG ESSEN   (Germany)

^d HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84958525795     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45455-1_30     Document Type: Conference Paper

References (17)

1. M. Daberkow, C. Fieker, J. Klüners, M. Pohst, K. Roegner and K. Wildanger, KANT V4, in J. Symbolic Comp. 24 (1997), 267-283.
2. V. G. Drinfel’d and S. G. Vladut, Number of points of an algebraic curve, Funct. Anal. 17 (1983), 53-54.
3. N. D. Elkies, Explicit modular towers, Proceedings of the Thirty-Fifth Annual Allerton Conference on Communication, Control and Computing, T. Basar and A. Vardy, eds. (1997), 23-32.
4. N. D. Elkies, Explicit towers of Drinfeld modular curves. Proceedings of the 3rd European Congress of Mathematics, Barcelona, 7/2000.
5. A. Garcia and H. Stichtenoth, A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound, Invent. Math. 121 (1995), 211-222.
6. A. Garcia and H. Stichtenoth, On the asymptotic behaviour of some towers of function fields over finite fields, J. Number Theory 61, (1996), 248-273.
7. A. Garcia and H. Stichtenoth, Asymptotically good towers of function fields over finite fields, C. R. Acad. Sci. Paris I 322 (1996), 1067-1070.
8. A. Garcia and H. Stichtenoth, Skew pyramids of function fields are asymptotically bad, in “Coding Theory, Cryptography and Related Topics”, Proceedings of a Conference in Guanajuato, 1998 (J. Buchmann et al, Eds.) 111-113, Springer-Verlag, Berlin 2000.
9. A. Garcia and H. Stichtenoth, On tame towers over finite fields, preprint (2001).
10. A. Garcia, H. Stichtenoth and M. Thomas, On towers and composita of towers of function fields over finite fields. Finite Fields Appl. 3 (1997), no. 3, 257-274.
11. Y. Ihara, Some remarks on the number of rational points of algebraic curves over finite fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), 721-724.
12. H. W. Lenstra, ., On a Problem of Garcia, Stichtenoth, and Thomas, To appear in Finite Fields Appl.
13. D. Lorenzini, An invitation to arithmetic geometry. Graduate Studies in Mathematics, 9. American Mathematical Society, Providence, RI, 1996.
14. H. Maharaj, H. Stichtenoth and J. Wulftange, On a Problem of Garcia, Stichtenoth, and Thomas II, In preparation.
15. H. Niederreiter and C. P. Xing, Rational Points on Curves over Finite Fields: Theory and Applications, Cambridge University Press, Cambridge, 2001.
16. H. Stichtenoth. Algebraic Function Fields and Codes, Springer Universitext. Berlin, Heidelberg, New York, 1993.
17. M.A. Tsfasman, S.G. Vladut and T. Zink, Modular curves, Shimura curves and Goppa codes better than the Varshamov-Gilbert bound. Math. Nachr. 109 (1982), 21-28.