Abstract
In this paper, we complete the classification of the caps in \(\text{ PG }(n,q)\) 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 \(\text{ PG }(5,3)\) related to the Mathieu group \(M_{12}\), a set of three noncollinear points in \(\text{ PG }(2,q)\) and some examples related to hyperovals of projective planes.
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Acknowledgements
The second author, Mou Gao, is supported by the National Science Foundation of China (Grant No. 12001083), and the State Scholarship Fund (File No. 201806065052).
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: The Art of Combinatorics – A Volume in Honour of Aart Blokhuis”.
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De Bruyn, B., Gao, M. A characterization of the Coxeter cap. Des. Codes Cryptogr. 90, 1963–1981 (2022). https://doi.org/10.1007/s10623-021-00855-x
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DOI: https://doi.org/10.1007/s10623-021-00855-x