On KM-arcs in non-Desarguesian projective planes

In this paper we investigate KM-arcs in non-Desarguesian projective planes. We provide a construction of a KM-arc in every Hall plane of even order, and we classify all KM-arcs in the known projective planes of order 16. In particular, we find several examples of KM-arcs with non-concurrent t -secan...

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Veröffentlicht in:	Designs, codes, and cryptography codes, and cryptography, 2019-09, Vol.87 (9), p.2129-2137
1. Verfasser:	Vandendriessche, Peter
Format:	Artikel
Sprache:	eng
Schlagworte:	Circuits Coding and Information Theory Computer Science Concurrency Cryptology Data Structures and Information Theory Discrete Mathematics in Computer Science Information and Communication Planes
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Zusammenfassung:	In this paper we investigate KM-arcs in non-Desarguesian projective planes. We provide a construction of a KM-arc in every Hall plane of even order, and we classify all KM-arcs in the known projective planes of order 16. In particular, we find several examples of KM-arcs with non-concurrent t -secants, showing that the famous result on their concurrency does not holds in non-Desarguesian planes.
ISSN:	0925-1022 1573-7586
DOI:	10.1007/s10623-019-00606-z