Embedding 1-Factorizations of K (n) in PG(2,32)

作者：Faina Giorgio^*; Parrettini Cristiano; Pasticci Fabio

来源：Graphs and Combinatorics, 2013, 29(4): 883-892.

DOI：10.1007/s00373-012-1166-y

• 1-Factorizations
• Galois planes
• Hyperfocused arcs

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 a parts per thousand currency sign 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.

• 出版日期2013-7