OFFSET
0,1
REFERENCES
J. W. P. Hirschfeld, Linear codes and algebraic codes, pp. 35-53 of F. C. Holroyd and R. J. Wilson, editors, Geometrical Combinatorics. Pitman, Boston, 1984. See N_2(g) on page 51.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Robin Visser, Incomplete table of n, a(n) for n = 0..50.
L. E. Dickson, Quartic Curves Modulo 2, Trans. Amer. Math. Soc. 16 (1915), no. 2, 111-120.
Jean-Pierre Serre, Sur le nombre des points rationnels d'une courbe algébrique sur un corps fini, C. R. Acad. Sci. Paris Ser. I Math. 296 (1983), no. 9, 397-402.
M. Tsfasman, S. Vlǎduţ, and D. Nogin, Algebraic Geometric Codes: Basic Notions, Math. Surveys Monogr., 139 American Mathematical Society, Providence, RI, 2007. xx+338 pp.
G. van der Geer, E. W. Howe, K. E. Lauter, and C. Ritzenthaler, Tables of Curves with Many Points.
J. H. van Lint and G. van der Geer, Introduction to Coding Theory and Algebraic Geometry, DMV Sem., 12 Birkhäuser Verlag, Basel, 1988. 83 pp.
C. Xing and H. Niederreiter, Drinfeld Modules of Rank 1 and Algebraic Curves with Many Rational Points, Monatsh. Math. 127 (1999), no. 3, 219-241.
EXAMPLE
For n = 3, Dickson (1915) proved that the genus 3 quartic curve given by x^3*y + x^2*y^2 + x*z^3 + x^2*z^2 + y^3*z + y*z^3 = 0 with 7 rational points attains the maximal number of points for a genus 3 curve over GF(2), thus a(3) = 7. - Robin Visser, Aug 17 2023
CROSSREFS
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
Edited by Robin Visser, Aug 16 2023, adding terms a(10)-a(11) computed by Serre.
STATUS
approved