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https://doi.org/10.1016/j.jcta.2004.06.005
Title: | On Mathon's construction of maximal arcs in Desarguesian planes II | Authors: | Fiedler, F. Leung, K.H. Xiang, Q. |
Keywords: | Arc Linearized polynomial Maximal arc Moore determinant Quadratic form |
Issue Date: | Oct-2004 | Citation: | Fiedler, F., Leung, K.H., Xiang, Q. (2004-10). On Mathon's construction of maximal arcs in Desarguesian planes II. Journal of Combinatorial Theory. Series A 108 (1) : 99-122. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jcta.2004.06.005 | Abstract: | In a recent paper, Mathon (J. Combin. Theory (A) 97 (2002) 353) 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 (⌊s/m⌋+1). This confirms our conjecture in (Fiedler et al. (Adv. Geom. (2003) (Suppl.) S119)). 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 ⌊m/2⌋+1 or ⌊m/2⌋+2. © 2004 Elsevier Inc. All rights reserved. | Source Title: | Journal of Combinatorial Theory. Series A | URI: | http://scholarbank.nus.edu.sg/handle/10635/103722 | ISSN: | 00973165 | DOI: | 10.1016/j.jcta.2004.06.005 |
Appears in Collections: | Staff Publications |
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