Incidence Matrices of Polarized Projective Spaces

2013/04/23 by Chunlei Liu, Liu, Chunlei, Haode Yan +1
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Matrix Theory and Algorithms #Number Theory (math.NT) #graph theory and CDMA systems #math.NT

paper · pdf · doi:10.48550/arxiv.1304.6218

arxiv created 2013/04/23 · openalex publication_date 2013/04/23 · arxiv updated 2013/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we first define a non-degenerate symmetric bilinear form on Fq⁴. Then we get an incidence matrix G of Fq⁴ by the bilinear form. By its corresponding quadratic form Q, the lines of Fq⁴ are classified as isotropic and anisotropic lines. Under this classification, we can get two sub-matrices of G and prove their 2-rank. Key words and phrases: finite field, quadratic form, incidence matrix.

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