On blocking sets in affine planes |
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Authors: | Luigia Berardi Franco Eugeni |
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Affiliation: | (1) Istituto di Matematica Applicata, Facolta di Ingegneria, L'Aquila, Italia |
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Abstract: | Denote byq an affine plane of order q. In the desarguesian case q=AG(2,q), q 5(q= ph, p prime), we prove that the smallest cardinality of a blocking set is 2q–1. In any arbitrary affine plane q (desarguesian or not) with q5, for any integer k with 2q–1 k(q–1)2, we construct a blocking set S with ¦S¦=k. For an irreducible blocking set S of q we determine the upper bound S [qq]+1. We prove that if q contains a blocking set S which is irreducible with its complementary blocking set, then necessarily q=AG(2, 4) and S is uniquely determined. Finally we introduce techniques to obtain blocking sets in AG(2, q) and in PG(2, q).Research partially supported by G.N.S.A.G.A. (CNR) |
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