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

被引：9

作者：

Sboui, Adnen ^{[1
,2
]}

机构：

[1] Math Campll Univ Caen, CNRS, LMNO, UMR 6139, F-14000 Caen, France

[2] Fac Sci Tunis, Dept Math, Tunis 1060, Tunisia

来源：

DISCRETE MATHEMATICS | 2009年 / 309卷 / 16期

关键词：

Hyperplane arrangements; Hypersurfaces; Rational points; Homogeneous polynomials; Projective Reed-Muller codes;

D O I：

10.1016/j.disc.2009.03.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study first some arrangements of hyperplanes in the n-dimensional projective space P-n(F-q). Then we compute, in particular, the second and the third highest numbers of rational points on hypersurfaces of degree d. As an application of our results, we obtain some weights of the Generalized Projective Reed-Muller codes PRM(q, d, n). We also list all the homogeneous polynomials reaching such numbers of zeros and giving the correspondent weights. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：5048 / 5059

页数：12

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