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(q-1)(q+1).

Abstract A lower bound on the minimum degree of the plane algebraic curves containing every point in a large point-set 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.

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.

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.

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 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).

Let Γ ′ be a subgraph of a graph Γ. We define a down-link 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 down-links in general and prove that any (Kv, Γ)-design might be down-linked to a (Kn, Γ ′)-design, provided that n is suitably chosen. We also investigate in detail down-links to P3-designs, 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 down-links from balanced Γ-designs to P3-designs, improving on the aforementioned bound.

No regular hyperoval of the Desarguesian affine plane AG(2,2^(2h)), with h> 1, is inherited by a dual André plane of order 2^(2h) and dimension 2 over its kernel.

Dedicated to Professor Adriano Barlotti on the occasion of his 80th birthday Abstract. We construct a new ovoid of the polar space arising from the Hermitian surface of PG(3,#2) with q ̂ 5 odd. The automorphism group Γ of such an ovoid has a normal cyclic subgroup Φ of order ^ (q + 1) such that Γ/Φ ^ PGL(2, q). Furthermore, Γ has three orbits on the ovoid, one of size q + 1 and two of size \q(q — \)(q + 1).