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Further results on fibre products of Kummer covers and curves with many points over finite fields
1. | Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Dumlupnar Bulvar, 06800, Ankara, Turkey |
2. | Department of Mathematics, Atlm University, Incek, Golbas, 06836, Ankara, Turkey |
3. | Department of Mathematics, Hacettepe University, Beytepe, 06800, Ankara, Turkey |
References:
[1] |
A. Garcia and A. Garzon, On Kummer covers with many rational points over finite fields, J. Pure Appl. Algebra, 185 (2003), 177-192.
doi: 10.1016/S0022-4049(03)00110-5. |
[2] |
G. van der Geer and M. van der Vlugt, Tables of curves with many points, Math. Comput., 69 (2000), 797-810.
doi: 10.1090/S0025-5718-99-01143-6. |
[3] |
J. W. P. Hirschfeld, Projective Geometries over Finite Fields, 2nd edition, The Clarendon Press, New York, 1998. |
[4] |
J. W. P. Hirschfeld, G. Korchmáros and F. Torres, Algebraic Curves over a Finite Field, Princeton Univ. Press, Princeton, 2008. |
[5] |
B. Huppert and N. Blackburn, Finite Groups II Springer-Verlag, New York, 1981. |
[6] |
M. Q. Kawakita, Kummer curves and their fibre products with many rational points, Appl. Algebra Engrg. Comm. Comput., 14 (2003), 55-64. |
[7] |
H. Niederreiter and C. Xing, Rational Points on Curves over Finite Fields, Cambridge Univ. Press, Cambridge, 2001.
doi: 10.1017/CBO9781107325951. |
[8] |
H. Niederreiter and C. Xing, Algebraic Geometry in Coding Theory and Cryptography, Princeton Univ. Press, Princeton, 2009. |
[9] |
F. Özbudak and H. Stichtenoth, Curves with many points and configurations of hyperplanes over finite fields, Finite Fields Appl., 5 (1999), 436-449.
doi: 10.1006/ffta.1999.0262. |
[10] |
F. Özbudak and B. G. Temür, Finite number of fibre products of Kummer covers and curves with many points over finite fields, Des. Codes Crypt., 70 (2014), 385-404.
doi: 10.1007/s10623-012-9706-2. |
[11] |
H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993. |
[12] |
M. A. Tsfasman, S. G. Vlădut and D. Nogin, Algebraic Geometric Codes: Basic Notions, Amer. Math. Soc., Providence, 2007.
doi: 10.1090/surv/139. |
[13] |
, Manypoints-Table of Curves with Many Points, available online at http://www.manypoints.org |
show all references
References:
[1] |
A. Garcia and A. Garzon, On Kummer covers with many rational points over finite fields, J. Pure Appl. Algebra, 185 (2003), 177-192.
doi: 10.1016/S0022-4049(03)00110-5. |
[2] |
G. van der Geer and M. van der Vlugt, Tables of curves with many points, Math. Comput., 69 (2000), 797-810.
doi: 10.1090/S0025-5718-99-01143-6. |
[3] |
J. W. P. Hirschfeld, Projective Geometries over Finite Fields, 2nd edition, The Clarendon Press, New York, 1998. |
[4] |
J. W. P. Hirschfeld, G. Korchmáros and F. Torres, Algebraic Curves over a Finite Field, Princeton Univ. Press, Princeton, 2008. |
[5] |
B. Huppert and N. Blackburn, Finite Groups II Springer-Verlag, New York, 1981. |
[6] |
M. Q. Kawakita, Kummer curves and their fibre products with many rational points, Appl. Algebra Engrg. Comm. Comput., 14 (2003), 55-64. |
[7] |
H. Niederreiter and C. Xing, Rational Points on Curves over Finite Fields, Cambridge Univ. Press, Cambridge, 2001.
doi: 10.1017/CBO9781107325951. |
[8] |
H. Niederreiter and C. Xing, Algebraic Geometry in Coding Theory and Cryptography, Princeton Univ. Press, Princeton, 2009. |
[9] |
F. Özbudak and H. Stichtenoth, Curves with many points and configurations of hyperplanes over finite fields, Finite Fields Appl., 5 (1999), 436-449.
doi: 10.1006/ffta.1999.0262. |
[10] |
F. Özbudak and B. G. Temür, Finite number of fibre products of Kummer covers and curves with many points over finite fields, Des. Codes Crypt., 70 (2014), 385-404.
doi: 10.1007/s10623-012-9706-2. |
[11] |
H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993. |
[12] |
M. A. Tsfasman, S. G. Vlădut and D. Nogin, Algebraic Geometric Codes: Basic Notions, Amer. Math. Soc., Providence, 2007.
doi: 10.1090/surv/139. |
[13] |
, Manypoints-Table of Curves with Many Points, available online at http://www.manypoints.org |
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