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23
Algebraic curves and maximal arcs
 JOURNAL OF ALGEBRAIC COMBINATORICS
, 2008
"... Abstract A lower bound on the minimum degree of the plane algebraic curves containing every point in a large pointset K of the Desarguesian plane PG(2,q) is obtained. The case where K is a maximal (k, n)arc is considered in greater depth. ..."
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Abstract A lower bound on the minimum degree of the plane algebraic curves containing every point in a large pointset K of the Desarguesian plane PG(2,q) is obtained. The case where K is a maximal (k, n)arc is considered in greater depth.
Ovoids of the Hermitian surface in odd characteristic
 Advances in Geometry
, 2003
"... Dedicated to Professor Adriano Barlotti on the occasion of his 80th birthday
We construct a new ovoid of the polar space arising from the Hermitian surface of
PG(3,q^2) with q>5 odd. The automorphism group G of such an ovoid has a normal cyclic
subgroup F of order 1/2(q+1) such that ..."
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Dedicated to Professor Adriano Barlotti on the occasion of his 80th birthday
We construct a new ovoid of the polar space arising from the Hermitian surface of
PG(3,q^2) with q>5 odd. The automorphism group G of such an ovoid has a normal cyclic
subgroup F of order 1/2(q+1) such that G/F~PGL(2,q). Furthermore, G has three orbits on
the ovoid, one of size q+1 and two of size 1/2q(q1)(q+1).
LDPC codes from Singer cycles
 DISCRETE APPLIED MATHEMATICS
, 2009
"... The main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block codes—characterised by admitting a sparse parity check matrix—with ..."
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The main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block codes—characterised by admitting a sparse parity check matrix—with good correction capabilities. In the present paper the orbits of subspaces of a finite projective space under the action of a Singer cycle are investigated.
On the intersection of Hermitian surfaces
 J. GEOM.
"... We provide a description of the conﬁguration arising from intersection of two Hermitian surfaces in
PG(3, q), provided that the linear system they generate contains at least a degenerate variety.
..."
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We provide a description of the conﬁguration arising from intersection of two Hermitian surfaces in
PG(3, q), provided that the linear system they generate contains at least a degenerate variety.
Line Polar Grassmann Codes of Orthogonal Type
"... Abstract Polar Grassmann codes of orthogonal type have been introduced in ..."
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Abstract Polar Grassmann codes of orthogonal type have been introduced in
Downlinking (Kv, Γ)designs to P3designs
"... Let Γ ′ be a subgraph of a graph Γ. We define a downlink from a (Kv, Γ)design B to a (Kn, Γ ′)design B ′ as an injective map f: B → B ′ mapping any block of B into one of its subgraphs. This is a new concept, closely related with both the classical notion of embedding and the more recent one of s ..."
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Let Γ ′ be a subgraph of a graph Γ. We define a downlink from a (Kv, Γ)design B to a (Kn, Γ ′)design B ′ as an injective map f: B → B ′ mapping any block of B into one of its subgraphs. This is a new concept, closely related with both the classical notion of embedding and the more recent one of sampling. In the present paper we study downlinks in general and prove that any (Kv, Γ)design might be downlinked to a (Kn, Γ ′)design, provided that n is suitably chosen. We also investigate in detail downlinks to P3designs, P3 being the path with 3 vertices, proving that it is always possible to take n ≤ v + 3. Furthermore, for several classes of graphs Γ, we provide explicit constructions of downlinks from balanced Γdesigns to P3designs, improving on the aforementioned bound.
An algorithm for constructing some maximal arcs in PG(2, q²)
, 2007
"... In 1974, J. Thas constructed a new class of maximal arcs for the Desarguesian plane of order q². The construction relied upon the existence of a regular spread of tangent lines to an ovoid in PG(3, q) and, in particular, it does apply to the Suzuki T.its ovoid. In this paper, we describe an algorith ..."
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In 1974, J. Thas constructed a new class of maximal arcs for the Desarguesian plane of order q². The construction relied upon the existence of a regular spread of tangent lines to an ovoid in PG(3, q) and, in particular, it does apply to the Suzuki T.its ovoid. In this paper, we describe an algorithm for obtaining a possible representation of such arcs in PG(2, q²).
Collineation groups of the intersection of two classical unitals
 J. COMBIN DESIGNS
, 2001
"... ..."
Looking for ovoids of the Hermitian surface
"... In this note we introduce a computational approach to the construction of ovoids of the Hermitian surface and present some related experimental results. ..."
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In this note we introduce a computational approach to the construction of ovoids of the Hermitian surface and present some related experimental results.
Results 1  10
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23