Incidence Matrices of Finite Quadratic Spaces

2013/03/14 by Chunlei Liu, Yan Liu, Liu, Chunlei +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #DNA and Biological Computing #Error Correcting Code Techniques #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems #math.NT

paper · pdf · doi:10.48550/arxiv.1303.3385

openalex publication_date 2013/03/14 · arxiv created 2013/03/18 · arxiv updated 2013/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first prove the 2-rank of full incidence matrix of PG(n,q) with q an odd prime power. Then by the quadratic form defined on PG(n,q), the points of it are classified as isotropic and anisotropic points. We divide the full incidence matrix into four sub-matrices. Then by using the software package Magma, we give a general conjecture for the 2-rank of sub-matrices of the full incidence matrix in PG(n,q) and prove it in the case of n=1, 2.

Related

• Incidence Matrices of Polarized Projective Spaces
• Some p-ranks related to a conic in PG(2,q)
• Incidence matrices for the class O₆ of lines external to the twisted cubic in PG(3,q)
• Twisted cubic and point-line incidence matrix in PG(3,q)
• Twisted cubic and plane-line incidence matrix in PG(3,q)