A005527 Maximal number of rational points on a curve of genus n over GF(2). (Formerly M2388)

3, 5, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14

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

Table of n, a(n) for n=0..11.

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

Sequence in context: A036496 A196112 A009004 * A285173 A009005 A362018

Adjacent sequences: A005524 A005525 A005526 * A005528 A005529 A005530

Keyword

nonn,more

Author

N. J. A. Sloane.

Extensions

Edited by Robin Visser, Aug 16 2023, adding terms a(10)-a(11) computed by Serre.

Status

approved