Paper Info
Title
Special numbers of rational points on hypersurfaces in the n-dimensional projective space over a finite field
Abstract
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.
Year
DOI
Venue
2009
10.1016/j.disc.2009.03.021
Discrete Mathematics
Keywords
Field
DocType
projective reed-muller codes,rational points,hyperplane arrangements,homogeneous polynomials,. hyperplane arrangements,projective reed–muller codes,projective reed-muller codes. 1,hypersurfaces,rational point,finite field,arrangement of hyperplanes,projective space,reed muller code
Projective line,Combinatorics,Twisted cubic,Complex projective space,Rational point,Quaternionic projective space,Collineation,Mathematics,Rational normal curve,Projective space
Journal
Volume
Issue
ISSN
309
16
Discrete Mathematics
Citations 
PageRank 
References 
8
0.76
6
Authors
1
Name
Order
Citations
PageRank
Adnen Sboui1252.75