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**publisher and metadata sources**).The natural geometric setting of quadrics commuting with a Hermitian surface of ${\rm PG}(3,q^2)$ , q odd, is adopted and a hemisystem on the Hermitian surface ${\cal H}(3,q^2)$ admitting the group… Continue Reading

Let L be a general linear complex in PG(3, q) for any prime power q. We show that when GF(q) is extended to GF(q2), the extended lines of L cover a non-singular Hermitian surface H ≅ H(3, q2) of… Continue Reading

For the Hermitian curve H defined over the finite field , we give a complete classification of Galois coverings of H of prime degree. The corresponding quotient curves turn out to be special cases of… Continue Reading

AbstractThe number N of rational points on an algebraic curve of genus g over a finite field
$${\mathbb{F}}_q $$
satisfies the Hasse–Weil bound
$$N \leqslant q + 1 + 1g\sqrt q $$
. A curve that… Continue Reading

By exploring some geometry of Segre varieties and Veronese varieties, new families of non-linear maximum rank distance codes and optimal constant rank codes are provided.

For each proper divisordof (q − q + 1), withqan even power of a prime, maximal curves of genus 12q−q+1d−1that are Fq-covered by the Hermitian curve are constructed.

A new family of relative hemisystems on the generalized quadrangle $${\mathcal {H}}(3,q^2)$$H(3,q2) admitting a group of order $$q^2(q+1)$$q2(q+1) as automorphism group, is constructed. As a by… Continue Reading

Starting with carefully chosen sets of points in the Desarguesian affine plane AG(2, q2) and using an idea first formulated by E. Shult, several infinite families of translation ovoids of the… Continue Reading

We prove that, for q odd and n ≥ 3, the group G = O n (q 2) · 2 is maximal in either the orthogonal group O 2n (q) or the special orthogonal group SO 2n (q). The group G corresponds to the stabilizer… Continue Reading

Abstract The maximality of certain symplectic subgroups of unitary groups PS U n (K), n ≥ 4, (K any field admitting a non-trivial involutory automorphism) belonging to the class 𝒞5 of Aschbacher is… Continue Reading