2018/11/16 by Gábor Korchmáros, Korchmáros, Gábor, Federico Romaniello +3
Computer Science · Mathematics · #05E30 #561E20 #Affine transformation #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometry #Limits and Structures in Graph Theory #Mathematics #Point (geometry) #Pure mathematics #math.CO #msc:05E30 #msc:561E20
paper · pdf · doi:10.48550/arxiv.1811.06765
14 pages
openalex publication_date 2018/11/16 · openalex created_date 2018/11/29 · arxiv created 2021/02/05 · arxiv updated 2021/02/08 · openalex updated_date 2026/07/28
In the m-dimensional affine space AG(m,q) over the finite field \mathbbFq of odd order q, the analogous of the Euclidean distance gives rise to a graph \mathfrakGm,q where vertices are the points of AG(m,q) and two vertices are adjacent if their (formal) squared Euclidean distance is a square in \mathbbFq (including the zero). In 2009, Kurz and Meyer made the conjecture that if m is even then \mathfrakGm,q is a strongly regular graph. In this paper we prove their conjecture.