A characterization of the Coxeter cap

A characterization of the Coxeter cap

In this paper, we complete the classification of the caps in PG ( n , q ) having the property that on every tangent line L , there exists a unique point distinct from the tangency point though which there is at least one secant line. The examples include the Coxeter cap in PG ( 5 , 3 ) related to th...

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Veröffentlicht in:Designs, codes, and cryptography codes, and cryptography, 2022-09, Vol.90 (9), p.1963-1981
Hauptverfasser: De Bruyn, B., Gao, M.
Format: Artikel
Sprache:eng
Schlagworte:
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Special Issue: The Art of Combinatorics – A Volume in Honour of Aart Blokhuis
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Zusammenfassung:In this paper, we complete the classification of the caps in PG ( n , q ) having the property that on every tangent line L , there exists a unique point distinct from the tangency point though which there is at least one secant line. The examples include the Coxeter cap in PG ( 5 , 3 ) related to the Mathieu group M 12 , a set of three noncollinear points in PG ( 2 , q ) and some examples related to hyperovals of projective planes.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-021-00855-x