2004/01/05 by Frank Fiedler, Fiedler, Frank, Ka Hin Leung +3
Computer Science · Engineering · Mathematics · #51E05 #51E21 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:51E05 #msc:51E21
paper · pdf · doi:10.48550/arxiv.math/0401030
21 pages
arxiv created 2004/01/05 · openalex publication_date 2004/01/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent paper [M], Mathon gives a new construction of maximal arcs which generalizes the construction of Denniston. In relation to this construction, Mathon asks the question of determining the largest degree of a non-Denniston maximal arc arising from his new construction. In this paper, we give a nearly complete answer to this problem. Specifically, we prove that when m≥ 5 and m≠ 9, the largest d of a non-Denniston maximal arc of degree 2d in PG(2,2m) generated by a p,1-map is (\floor m/2 +1). This confirms our conjecture in [FLX]. For p,q-maps, we prove that if m≥ 7 and m≠ 9, then the largest d of a non-Denniston maximal arc of degree 2d in PG(2,2m) generated by a p,q-map is either \floor m/2 +1 or \floorm/2 +2.