P. Santonastaso

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 $PG (n - 1, q)$ denote the $(n - 1)$ -dimensional projective space over $F_{q}$ . We investigate the intersection of two Desarguesian $(h - 1)$ -spreads of $\mathrm{PG}(kh…

On pseudo-arcs from normal rational curve and additive MDS codes

Francesco Pavese, Paolo Santonastaso

Let $PG (k - 1, q)$ be the $(k - 1)$ -dimensional projective space over the finite field $F_{q}$ . An arc in $PG (k - 1, q)$ 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 $J_{q} (n, m, t)$ . In this graph, the vertices correspond to the $m$ -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…

Skew polynomial representations of matrix algebras and applications to coding theory

Alessandro Neri, Paolo Santonastaso

We extend the existing skew polynomial representations of matrix algebras which are direct sum of matrix spaces over division rings. In this representation, the sum-rank distance b…

Adjoint and duality for rank-metric codes in a skew polynomial framework

José Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro +1

Skew polynomial rings provide a fundamental example of noncommutative principal ideal domains. Special quotients of these rings yield matrix algebras that play a central role in th…

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…

math.NT2025

Blocking Sets and Power Residue Modulo Integers with Bounded Number of Prime Factors

Bhawesh Mishra, Paolo Santonastaso

Let $q$ be an odd prime and $k$ be a natural number. We show that a finite subset of integers $S$ that does not contain any perfect $q^{t h}$ power, contains a $q^{t h}$ power residu…

Asymptotically optimal cyclic subspace codes

Chiara Castello, Paolo Santonastaso

Subspace codes, and in particular cyclic subspace codes, have gained significant attention in recent years due to their applications in error correction for random network coding.…

math.NT2025

Prime Power Residues and Blocking Sets

Bhawesh Mishra, Paolo Santonastaso

Let $q$ be a fixed odd prime. We show that a finite subset $B$ of integers, not containing any perfect $q^{t h}$ power, contains a $q^{t h}$ power modulo almost every prime if and on…

Invariants for sum-rank metric codes

Paolo Santonastaso, Ferdinando Zullo

The code equivalence problem is central in coding theory and cryptography. While classical invariants are effective for Hamming and rank metrics, the sum-rank metric, which unifies…

On line-parallelisms of PG(3, q)

Francesco Pavese, Paolo Santonastaso

Let $PG (3, q)$ denote the three-dimensional projective space over the finite field with $q$ elements. A line-spread of $PG (3, q)$ is a collection $S$ of…