14 papers
Unbalanced distance-biregular graphs with girth deficiency two
Sebastiano Argenti, Alessandro Siciliano
Let be a distance-biregular graph with even diameter and girth . On the edge-set we define relations that form an association scheme; this is done by consid…
The association scheme on the set of flags of a finite generalized quadrangle
Francesco Colangelo, Giusy Monzillo, Alessandro Siciliano
In this paper, the association scheme defined on the flags of a finite generalized quadrangle is considered. All possible fusions of this scheme are listed, and a full description…
Classifying pseudo-ovals, translation generalized quadrangles, and elation Laguerre planes of small order
Giusy Monzillo, Tim Penttila, Alessandro Siciliano
We provide classification results for translation generalized quadrangles of order less or equal to , and hence, for all incidence geometries related to them. The results consi…
Classification of spreads of Tits quadrangles of order 64
Giusy Monzillo, Tim Penttila, Alessandro Siciliano
Brown et al. provide a representation of a spread of the Tits quadrangle , an oval of , even, in terms of a certain family of …
Eggs in finite projective spaces and unitals in translation planes
Giusy Monzillo, Tim Penttila, Alessandro Siciliano
Inspired by the connection between ovoids and unitals arising from the Buekenhout construction in the André/Bruck-Bose representation of translation planes of dimension at most two…
Reconstructing a generalized quadrangle from the Penttila-Williford class association scheme
Giusy Monzillo, Alessandro Siciliano
Penttila and Williford constructed a class association scheme from a generalized quadrangle with a doubly subtended subquadrangle. We show that an association scheme with appro…
Classification of flocks of the quadratic cone in PG(3,64)
Giusy Monzillo, Tim Penttila, Alessandro Siciliano
Flocks are an important topic in the field of finite geometry, with many relations with other objects of interest. This paper is a contribution to the difficult problem of classify…
Pseudo-ovals of elliptic quadrics as Delsarte designs of association schemes
John Bamberg, Giusy Monzillo, Alessandro Siciliano
A - of a finite projective space over a finite field of odd order is a configuration of equidimensional subspaces that is essentially equivalent to a translation…
On the isomorphism of certain primitive -polynomial not -polynomial association schemes
Giusy Monzillo, Alessandro Siciliano
In 2011, Penttila and Williford constructed an infinite new family of primitive -polynomial 3-class association schemes, not arising from distance regular graphs, by exploring t…
Puncturing maximum rank distance codes
Bence Csajbók, Alessandro Siciliano
We investigate punctured maximum rank distance codes in cyclic models for bilinear forms of finite vector spaces. In each of these models we consider an infinite family of linear m…
Non-linear maximum rank distance codes in the cyclic model for the field reduction of finite geometries
Nicola Durante, Alessandro Siciliano
In this paper we construct infinite families of non-linear maximum rank distance codes by using the setting of bilinear forms of a finite vector space. We also give a geometric des…
Unitals of PG(2,q^2) containing conics
N. Durante, A. Siciliano
A unital in PG(2,q^2) is a set U of q^3+1 points such that each line meets U in 1 or q+1 points. The well known example is the classical unital consisting of all absolute points of…
The geometry of elation groups of a finite projective space
N. Durante, A. Siciliano
We study the geometry of point-orbits of elation groups with a given center and axis of a finite projective space. We show that there exists a 1-1 correspondence from conjugacy cla…
The known maximal partial ovoids of size of Q(4,q)
Kris Coolsaet, Jan De Beule, Alessandro Siciliano
We present a description of maximal partial ovoids of size of the parabolic quadric $\q(4,q)$ as sharply transitive subsets of $\SL(2,q)$ and show their connection with spr…