Embedding 1-Factorizations of K
n
in PG(2, 32) |
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Authors: | Giorgio Faina Cristiano Parrettini Fabio Pasticci |
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Institution: | 1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, via Vanvitelli 1, 06123, Perugia, Italy
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Abstract: | 1-Factorizations of the complete graph K n embedded in a finite Desarguesian projective plane PG(2, q), q even, are hyperfocused arcs of size n. The classification of hyperfocused arcs is motivated by applications to 2-level secret sharing schemes. So far it has been done for q ≤ 16, and for special types of hyperfocused arcs. In this paper the case q = 32 is investigated and the following two results are proven. (i) Uniqueness of hyperfocused 12-arcs, up to projectivities. (ii) Non-existence of hyperfocused 14-arcs. |
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