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

@article{Sboui2009SpecialNO,
  title={Special numbers of rational points on hypersurfaces in the n-dimensional projective space over a finite field},
  author={Adnen Sboui},
  journal={Discrete Mathematics},
  year={2009},
  volume={309},
  pages={5048-5059}
}
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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