Let PG ( r , q ) {\operatorname{PG}(r,q)} be the r-dimensional projective space over the finite field GF ( q ) {\operatorname{GF}(q)} . A set 𝒳 {\mathcal{X}} of points of PG ( r , q ) {\operatorname{PG}(r,q)} is a cutting blocking... more
Let PG ( r , q ) {\operatorname{PG}(r,q)} be the r-dimensional projective space over the finite field GF ( q ) {\operatorname{GF}(q)} . A set 𝒳 {\mathcal{X}} of points of PG ( r , q ) {\operatorname{PG}(r,q)} is a cutting blocking set if for each hyperplane Π of PG ( r , q ) {\operatorname{PG}(r,q)} the set Π ∩ 𝒳 {\Pi\cap\mathcal{X}} spans Π. Cutting blocking sets give rise to saturating sets and minimal linear codes, and those having size as small as possible are of particular interest. We observe that from a cutting blocking set obtained in [20], by using a set of pairwise disjoint lines, there arises a minimal linear code whose length grows linearly with respect to its dimension. We also provide two distinct constructions: a cutting blocking set of PG ( 3 , q 3 ) {\operatorname{PG}(3,q^{3})} of size 3 ( q + 1 ) ( q 2 + 1 ) {3(q+1)(q^{2}+1)} as a union of three pairwise disjoint q-order subgeometries, and a cutting blocking set of PG ( 5 , q ) {\operatorname{PG}(5,...
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Research Interests: Mathematics and Geometry
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ABSTRACT
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We study Kestenband–Ebert partitions from a group-theoretic point of view. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 367–375, 1997
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New infinite families of hyperovals of the generalized quadrangle H(3,q^2) are provided. They arise in different geometric contexts. More precisely, we construct hyperovals by means of certain subsets of the projective plane called here... more
New infinite families of hyperovals of the generalized quadrangle H(3,q^2) are provided. They arise in different geometric contexts. More precisely, we construct hyperovals by means of certain subsets of the projective plane called here k-tangent arcs with respect to a Hermitian curve (Section 2), hyperovals arising from the geometry of an orthogonal polarity commuting with a unitary polarity (Section 3), hyperovals admitting the irreducible linear group PSL(2,7) as a subgroup of PGU(3,q^2), q=p^h, p=3,5or6(mod7) and h an odd integer (Section 4). Finally we construct hyperovals by means of the embedding of PSp(4,q)
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ABSTRACT Two new infinite families of hyperovals on the generalized quadrangle $\mathcal H (3,q^2), q$ H ( 3 , q 2 ) , q odd, are constructed.