Special numbers of rational points on hypersurfaces in the n-dimensional projective space over a finite field

  title={Special numbers of rational points on hypersurfaces in the n-dimensional projective space over a finite field},
  author={Adnen Sboui},
  journal={Discrete Mathematics},
Abstract. We study first some arrangements of hyperplanes in the n-dimensional projective space Pn(Fq). Then we compute, in particular, the second and the third highest numbers of rational points on hypersurfaces of degree d. As application of our results we obtain some weights of the Generalized Projective Reed-Muller codes PRM(q, d, n). And we also list all the homogeneous polynomials reaching such numbers of zeros and giving the correspondent weights. 

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Showing 1-10 of 10 references

On the number of points of some Hypersurfaces in F q

J.-P. Cherdieu, R. Rolland
Finite Fields and Their applications, • 1996
View 6 Excerpts
Highly Influenced

Tsfasman du 24 Juillet 1989, in journées Arithmétiques de Luminy

M.J.-P. Serre Lettre à
Juillet • 1989
View 8 Excerpts
Highly Influenced

Mac Williams: on generalized Reed-Muller codes and their relatives

P. Delsarte, J. M Goethals, F.J
Inform. Control • 1970
View 7 Excerpts
Highly Influenced

Projective Reed-Muller codes

IEEE Trans. Information Theory • 1991
View 4 Excerpts
Highly Influenced

Second highest number of points of hypersurfaces in Fnq

Finite Fields and Their Applications • 2007
View 1 Excerpt

Reed-Muller codes associated to projective algebraic varieties, ”Coding Theory and Algebraic geometry

Y. Aubry
Luminy • 1991
View 1 Excerpt

The parameters of projective Reed-Müller codes

Discrete Mathematics • 1990
View 3 Excerpts

Linear codes and modular curves

Y. I. Manin, S. Vladut
Itogi Nauki Tekhniki • 1984
View 3 Excerpts

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