12 citations · 19 across the 30 of their papers we have counts for
15 papers · 1 filter
On the autotopism groups and the equivalence of finite cyclic semifields
Paolo Santonastaso, Yue Zhou
Special cases of finite cyclic semifields were first constructed by Hughes and Kleinfeld in 1960, and later by Sandler in 1962 and Knuth in 1965. The general construction of cyclic…
Segre Varieties and Desarguesian Spreads
Antonio Cossidente, Giuseppe Marino, Francesco Pavese +2
Let denote the -dimensional projective space over . We investigate the intersection of two Desarguesian -spreads of $\mathrm{PG}(kh…
On pseudo-arcs from normal rational curve and additive MDS codes
Francesco Pavese, Paolo Santonastaso
Let be the -dimensional projective space over the finite field . An arc in is a set of points with the property that…
Chromatic Number of Grassmann Graphs and MRD codes
Jozefien D'haeseleer, Francesco Pavese, Paolo Santonastaso +1
In this paper we investigate the chromatic number of the Grassmann graphs and of their powers, denoted . In this graph, the vertices correspond to the -dimensional s…
The maximum number of nonzero weights of linear rank-metric codes
Chiara Castello, Paolo Santonastaso, Martin Scotti
We investigate the maximum number \( L_{\mathrm{rk}}(n, m, k, q) \) of distinct nonzero rank weights that an \( \mathbb{F}_{q^m} \)-linear rank-metric code of dimension \( k \) in…
Clubs in projective spaces and three-weight rank-metric codes
Jonathan Mannaert, Paolo Santonastaso, Ferdinando Zullo
Linear sets over finite fields are central objects in finite geometry and coding theory, with deep connections to structures such as semifields, blocking sets, KM-arcs, and rank-me…
On line-parallelisms of PG(3, q)
Francesco Pavese, Paolo Santonastaso
Let denote the three-dimensional projective space over the finite field with elements. A line-spread of is a collection of…
Quotients of skew polynomial rings: new constructions of division algebras and MRD codes
F. J. Lobillo, Paolo Santonastaso, John Sheekey
We achieve new results on skew polynomial rings and their quotients, including the first explicit example of a skew polynomial ring where the ratio of the degree of a skew polynomi…
Constructions and equivalence of Sidon spaces
Chiara Castello, Olga Polverino, Paolo Santonastaso +1
Sidon spaces have been introduced by Bachoc, Serra and Zémor in 2017 as the -analogue of Sidon sets. The interest on Sidon spaces has increased quickly, especially after the wor…
On the minimum size of linear sets
Sam Adriaensen, Paolo Santonastaso
Recently, a lower bound was established on the size of linear sets in projective spaces, that intersect a hyperplane in a canonical subgeometry. There are several constructions sho…
Cones from maximum -scattered linear sets and a stability result
Sam Adriaensen, Jonathan Mannaert, Paolo Santonastaso +1
This paper mainly focuses on cones whose basis is a maximum -scattered linear set. We start by investigating the intersection sizes of such cones with the hyperplanes. Then we a…
Clubs and their applications
Vito Napolitano, Olga Polverino, Paolo Santonastaso +1
Clubs of rank k are well-celebrated objects in finite geometries introduced by Fancsali and Sziklai in 2006. After the connection with a special type of arcs known as KM-arcs, they…
Classifications and constructions of minimum size linear sets
Vito Napolitano, Olga Polverino, Paolo Santonastaso +1
This paper aims to study linear sets of minimum size in the projective line, that is -linear sets of rank in admitting one point of weight on…
Two pointsets in and the associated codes
Vito Napolitano, Olga Polverino, Paolo Santonastaso +1
In this paper we consider two pointsets in arising from a linear set of rank contained in a line of : the first one is a linear blo…
Linear sets on the projective line with complementary weights
Vito Napolitano, Olga Polverino, Paolo Santonastaso +1
Linear sets on the projective line have attracted a lot of attention because of their link with blocking sets, KM-arcs and rank-metric codes. In this paper, we study linear sets ha…