Tables of curves with many points

Mathematics of Computation

Volumn 69, Issue 230, 2000, Pages 797-810

  Van Der Geer, Gerard ^a   Van Der Vlugt, Marcel ^b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b LEIDEN UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034384230     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-99-01143-6     Document Type: Article

References (77)

1. R. Auer: Ray class fields of global function fields with many rational places. Report University of Oldenburg, 1998.
2. L.E. Dickson: Geometrical and invariantive theory of quartic curves modulo 2. Am. J. Math. 37 (1915), 337-354
3. J. Doumen: Master's thesis. Leiden University, 1998.
4. N. Elkies: Private communication, 1997.
5. R. Fuhrmann, F. Torres: The genus of curves over finite fields with many rational points. Manuscripta Math. 89 (1996), 103-106. MR 96m:11046
6. R. Fuhrmann, F. Torres: The genus of curves over finite fields with many rational points. Manuscripta Math. 89 (1996), 103-106. MR 96m:11046
7. A. Garcia, H. Stichtenoth: A class of polynomials over finite fields. Preprint, 1998.
8. A. Garcia, H. Stichtenoth, C.P. Xing: On subfields of the Hermitian function field. Preprint 1998.
9. G. van der Geer, M. van der Vlugt: Curves over finite fields of characteristic 2 with many rational points. C.R. Acad. Sci. Paris 317, Série I (1993), 593-597. MR 94k:11068
10. G. van der Geer, M. van der Vlugt: Curves over finite fields of characteristic 2 with many rational points. C.R. Acad. Sci. Paris 317, Série I (1993), 593-597. MR 94k:11068
11. G. van der Geer, M. van der Vlugt: Generalized Hamming weights of codes and curves over finite fields with many points. In: Israel Math Conf. Proc. 9 (1996), 417-432. MR 96m:11047
12. G. van der Geer, M. van der Vlugt: Generalized Hamming weights of codes and curves over finite fields with many points. In: Israel Math Conf. Proc. 9 (1996), 417-432. MR 96m:11047
13. G. van der Geer, M. van der Vlugt: Quadratic forms, generalized Hamming weights of codes and curves with many points. J. of Number Theory 59 (1996), 20-36. MR 97i:11068
14. G. van der Geer, M. van der Vlugt: Quadratic forms, generalized Hamming weights of codes and curves with many points. J. of Number Theory 59 (1996), 20-36. MR 97i:11068
15. G. van der Geer, M. van der Vlugt: How to construct curves over finite fields with many points. In: Arithmetic Geometry, (Cortona 1994), F. Catanese Ed., Sympos. Math. 37 Cambridge Univ. Press, Cambridge, 1997, 169-189.
16. MR 98h:11077
17. q(g). Regularly updated tables at: http://www.wins.uva.nl/~geer.
18. G. van der Geer, M. van der Vlugt: Generalized Reed-Muller codes and curves with many points. J. of Number Theory 72 (1998) 257-268. CMP 99:04
19. G. van der Geer, M. van der Vlugt: Generalized Reed-Muller codes and curves with many points. J. of Number Theory 72 (1998) 257-268. CMP 99:04
20. G. van der Geer, M. van der Vlugt: Constructing curves over finite fields with many rational points by solving linear equations. Report W 97-29, Leiden University 1997.
21. V.D. Goppa : Codes on algebraic curves. Sov. Math. Dokl. 24 (1981), 170-172. MR 82k:94017
22. V.D. Goppa : Codes on algebraic curves. Sov. Math. Dokl. 24 (1981), 170-172. MR 82k:94017
23. J.P. Hansen: Group codes and algebraic curves. Mathematica Gottingensis, Schriftenreihe SFB Geometrie und Analysis, Heft 9, 1987.
24. G. Haché, D. Le Brigand: Effective construction of algebraic geometry codes. IEEE Trans. Inform. Theory 41 (1995), 1615-1628. MR 97g:94037
25. G. Haché, D. Le Brigand: Effective construction of algebraic geometry codes. IEEE Trans. Inform. Theory 41 (1995), 1615-1628. MR 97g:94037
26. J.P. Hansen, H. Stichtenoth: Group codes on certain algebraic curves with many rational points. Appl. Algebra Engrg. Comm. Comput. 1 (1990), 67-77. MR 96e:94023
27. J.P. Hansen, H. Stichtenoth: Group codes on certain algebraic curves with many rational points. Appl. Algebra Engrg. Comm. Comput. 1 (1990), 67-77. MR 96e:94023
28. Y. Ihara: Some remarks on the number of rational points of algebraic curves over finite fields. J. Fac. Sci. Tokyo 28 (1981), 721-724. MR 84c:14016
29. Y. Ihara: Some remarks on the number of rational points of algebraic curves over finite fields. J. Fac. Sci. Tokyo 28 (1981), 721-724. MR 84c:14016
30. K. Lauter: Ray class field constructions of curves over finite fields with many rational points. In: Algorithmic Number Theory (Talence 1996), H. Cohen Ed., Lecture Notes in Computer Science 1122, Springer, Berlin, 1996, 187-195. MR 98a:11076
31. K. Lauter: Ray class field constructions of curves over finite fields with many rational points. In: Algorithmic Number Theory (Talence 1996), H. Cohen Ed., Lecture Notes in Computer Science 1122, Springer, Berlin, 1996, 187-195. MR 98a:11076
32. 3 of genus 5 with 14 rational points. Preprint 1998.
33. K. Lauter: Improved upper bounds for the number of rational points on algebraic curves over finite fields. Preprint, University of Michigan, 1999.
34. 2 of genus 3, 4 and 5. IEEE Trans. Inform. Theory 41 (1995), 1643-1645. MR 97b:14032
35. 2 of genus 3, 4 and 5. IEEE Trans. Inform. Theory 41 (1995), 1643-1645. MR 97b:14032
36. H. Niederreiter, C. P. Xing: Quasi-random points and global function fields. In: Finite Fields and Applications, S.D. Cohen, H. Niederreiter Eds., Cambridge Univ. Press, Cambridge 1996, 269-296. MR 97j:11037
37. H. Niederreiter, C. P. Xing: Quasi-random points and global function fields. In: Finite Fields and Applications, S.D. Cohen, H. Niederreiter Eds., Cambridge Univ. Press, Cambridge 1996, 269-296. MR 97j:11037
38. H. Niederreiter, C. P. Xing: Explicit global function fields over the binary field with many rational places. Acta Arithm. 75 (1996), 383-396. MR 97d:11177
39. H. Niederreiter, C. P. Xing: Explicit global function fields over the binary field with many rational places. Acta Arithm. 75 (1996), 383-396. MR 97d:11177
40. H. Niederreiter, C. P. Xing: Cyclotomic function fields, Hubert class fields and global function fields with many rational places. Acta Arithm. 79 (1997), 59-76. MR 97m:11141
41. H. Niederreiter, C. P. Xing: Cyclotomic function fields, Hubert class fields and global function fields with many rational places. Acta Arithm. 79 (1997), 59-76. MR 97m:11141
42. H. Niederreiter, C. P. Xing: Drinfeld modules of rank 1 and algebraic curves with many rational points II. Acta Arithm. 81 (1997), 81-100. CMP 97:14
43. H. Niederreiter, C. P. Xing: Drinfeld modules of rank 1 and algebraic curves with many rational points II. Acta Arithm. 81 (1997), 81-100. CMP 97:14
44. H. Niederreiter, C. P. Xing: Global function fields fields with many rational points over the ternary field. Acta Arithm. 83 (1998), 65-86. MR 98j:11110
45. H. Niederreiter, C. P. Xing: Global function fields fields with many rational points over the ternary field. Acta Arithm. 83 (1998), 65-86. MR 98j:11110
46. H. Niederreiter, C. P. Xing: Algebraic curves with many rational points over finite fields of characteristic 2. To appear in: Proc. Number Theory Conference (Zakopane 1997), de Gruyter, Berlin.
47. H. Niederreiter, C. P. Xing: A general method of constructing global function fields with many rational places. To appear in: Algorithmic Number Theory (Portland 1998), Lecture Notes in Comp. Science, Springer, Berlin.
48. H. Niederreiter, C. P. Xing: Nets, (t, s)-sequences and algebraic geometry. To appear in Pseudo- and quasi-random point sets, P. Hellekalek, G. Larcher, Eds. Lecture Notes in Statistics, Springer, New York, 1998.
49. F. Özbudak, H. Stichtenoth: Curves with many points and configurations of hyperplanes over finite fields. Preprint 1998.
50. R. Schoof: Algebraic curves and coding theory. UTM 336, Univ. of Trento, 1990.
51. B. Segre: Introduction to Galois geometries. Atti Acad. Naz. Lincei (Mem. Cl. Sci. Fis. Mat. Natur.) 8 (1967), 133-236. MR 39:206
52. B. Segre: Introduction to Galois geometries. Atti Acad. Naz. Lincei (Mem. Cl. Sci. Fis. Mat. Natur.) 8 (1967), 133-236. MR 39:206
53. S. Sémirat: Genus theory for quadratic fields and applications. Preprint Université Paris VI, 1998.
54. J-P. Serre : Sur le nombre de points rationnels d'une courbe algébrique sur un corps fini. C.R. Acad. Sci. Paris 296, Série I (1983), 397-402. (= Oeuvres III, No. 128, 658-663). MR85b:14027; MR 89h:01109c
55. J-P. Serre : Sur le nombre de points rationnels d'une courbe algébrique sur un corps fini. C.R. Acad. Sci. Paris 296, Série I (1983), 397-402. (= Oeuvres III, No. 128, 658-663). MR85b:14027; MR 89h:01109c
56. J-P. Serre : Sur le nombre de points rationnels d'une courbe algébrique sur un corps fini. C.R. Acad. Sci. Paris 296, Série I (1983), 397-402. (= Oeuvres III, No. 128, 658-663). MR85b:14027; MR 89h:01109c
57. J-P. Serre : Sur le nombre de points rationnels d'une courbe algébrique sur un corps fini. C.R. Acad. Sci. Paris 296, Série I (1983), 397-402. (= Oeuvres III, No. 128, 658-663). MR85b:14027; MR 89h:01109c
58. q. Sém. de Théorie des Nombres de Bordeaux, 1982/83, exp. no. 22. (= Oeuvres III, No. 129, 664-668). MR 86d:11051; MR89h:01109c
59. q. Sém. de Théorie des Nombres de Bordeaux, 1982/83, exp. no. 22. (= Oeuvres III, No. 129, 664-668). MR 86d:11051; MR89h:01109c
60. q. Sém. de Théorie des Nombres de Bordeaux, 1982/83, exp. no. 22. (= Oeuvres III, No. 129, 664-668). MR 86d:11051; MR89h:01109c
61. q. Sém. de Théorie des Nombres de Bordeaux, 1982/83, exp. no. 22. (= Oeuvres III, No. 129, 664-668). MR 86d:11051; MR89h:01109c
62. q ? Résumé des Cours de 1983-1984. (=Oeuvres III, No. 132, 701-705). MR 89h:01109c
63. q ? Résumé des Cours de 1983-1984. (=Oeuvres III, No. 132, 701-705). MR 89h:01109c
64. q ? Résumé des Cours de 1983-1984. (=Oeuvres III, No. 132, 701-705). MR 89h:01109c
65. J-P. Serre: Rational points on curves over finite fields. Notes of lectures at Harvard University 1985.
66. J-P. Serre: Letter to G. van der Geer, September 1, 1997.
67. V. Shabat: Unpublished manuscript, University of Amsterdam, 1997/98.
68. H. Stichtenoth: Self-dual Goppa codes. J. Pure and Appl. Algebra 55 (1988), 199-211. MR 90a:11150
69. H. Stichtenoth: Self-dual Goppa codes. J. Pure and Appl. Algebra 55 (1988), 199-211. MR 90a:11150
70. q(z). In: Proc. 2nd Int. Workshop on Alg. and Comb. Coding Theory, Leningrad (1990), 203-206.
71. K.O. Stöhr, J. F. Voloch: Weierstrass points and curves over finite fields. Proc. London Math. Soc. 52 (1986), 1-19. MR 87b:14010
72. K.O. Stöhr, J. F. Voloch: Weierstrass points and curves over finite fields. Proc. London Math. Soc. 52 (1986), 1-19. MR 87b:14010
73. M. Suzuki: Private communication, 1998.
74. M. Wirtz : Konstruktion und Tabellen linearer Codes. Westfälische Wilhelms-Universität Münster, 1991.
75. J. Wolfmann: Nombre de points rationnels de courbes algébriques sur des corps finis associées à des codes cycliques. C.R. Acad. Sci. Paris 305, Série I (1987), 345 348. MR 88k:11025
76. J. Wolfmann: Nombre de points rationnels de courbes algébriques sur des corps finis associées à des codes cycliques. C.R. Acad. Sci. Paris 305, Série I (1987), 345 348. MR 88k:11025
77. C. P. Xing, H. Niederreiter: Drinfeld modules of rank I and algebraic curves with many rational points. Report Austrian Academy of Sciences, Vienna. 1996.