arXiv subjects

Giuseppe Marino

Publications and source records attributed to Giuseppe Marino.

At least 19 recordsLinked to original sources

arXiv2026

Discovery of an Eccentric Hot Super-Jupiter Leaving the Transiting Geometry of the Early-A-type star TOI-1355

Hot Jupiters orbiting hot stars ($T_\mathrm{eff} > 7000$ K) are suggested to have experienced high-eccentricity migration, often evidenced by the tendency for misaligned orbits, despite their circular orbits. In this paper, we present the discovery of TOI-1355 b: an eccentric ($e\sim0.22$) hot Jupiter with a mass of $m_{\mathrm{p}}\sim5.8M_J$ and a radius of $R_{\mathrm{p}}\sim 1.4R_J$ orbiting an A-type star with a period of about $2.17$ days, identified from the TESS transit survey and subsequent follow-up observations. We measured the stellar parameters using the data from the high-resolution spectrograph Seimei/GAOES-RV and obtained the planetary parameters from the photometric data acquired by TESS and ground-based telescopes. This is one of the rare eccentric hot Jupiters around hot stars. This system could be undergoing high-eccentricity migration. We detected nodal precession by measuring the change in its impact parameter. This implies that its transit will no longer be observable from the middle of 2033. Nevertheless, TOI-1355 b is anticipated to be a compelling target for future atmospheric observations, given the hint of atmospheric variability detected in this study.

astro-ph.EP↗

arXiv2026

Strongly regular graphs from hyperbolic quadrics and their maximal cliques

Let $Q^+(2n+1,q)$ be a hyperbolic quadric of $\PG(2n+1,q)$. Fix a generator $Π$ of the quadric. Define $\cG_n$ as the graph with as vertex set the points of $Q^+(2n+1,q)\setminus Π$ and two vertices adjacent if they either span a secant to $Q^+(2n+1,q)$ or a line contained in $Q^+(2n+1,q)$ meeting $Π$ non-trivially. Then such a construction defines a strongly regular graph, which is the complement of a (non-induced) subgraph of the collinearity graph of $Q^+(2n+1,q)$. In this paper, we directly compute the parameters of $\cG_n$, which is cospectral, when $q=2$, to the tangent graph $NO^+(2n+2,2)$, but it is non-isomorphic for $n\geq3$. We also classify the maximal cliques of $\cG_3$ for $q=2$, proving as a by-product the non-isomorphism with the graph $NO^+(8,2)$.

math.CO↗

arXiv2026

A geometric approach to generalized covering radii of linear codes

Covering problems in coding theory are closely related to finite geometry through the interpretation of the columns of parity-check matrices as point sets in finite vector spaces. Motivated by the recent notion of generalized covering radii of linear codes introduced by Elimelech, Firer and Schwartz, we develop a geometric framework for these parameters. We introduce $(ρ,t)$-saturating sets and show that they are precisely the finite-geometric counterparts of linear codes whose $t$-th generalized covering radius is at most $ρ$. We study the structure of these sets and show that the extremal case $ρ=t$ coincides with the notion of $t$-strong blocking sets. Thus, $(ρ,t)$-saturating sets interpolate between classical saturating sets and strong blocking sets. We provide several equivalent formulations, including affine and dual Grassmannian criteria, derive lower bounds on their size, and give constructions from strong blocking sets, graphs and projective configurations.

math.CO↗

arXiv2026

TOI-2155 b: A Massive Brown Dwarf or a Very Low-Mass Star?

We present TOI-2155\,b, a massive transiting companion, discovered using data from NASA's Transiting Exoplanet Survey Satellite (TESS) mission and confirmed with ground-based RV measurements from the Tillinghast Reflector Echelle Spectrograph (TRES). We also analyze ground-based follow-up photometric data from the Wendelstein Observatory (WST), Las Cumbres Observatory Global Telescope (LCOGT), and Wild Boar Remote Observatory (WBR). TOI-2155\,b is a short-period companion with {$P= 3.7246950 \pm{0.0000014}$}~days. The radius and mass of TOI-2155\,b are found to be $R_b = 0.972^{+0.009}_{-0.008} \,\mathrm{R_J}$ and $M_b = 80.6^{+1.0}_{-1.1} \,\mathrm{M_J}$, respectively, corresponding to a density of {$ρ_b= 109^{+3.1}_{-3.3}$ g cm$^{-3}$}. The F-type subgiant host star has an effective temperature of $T_{\rm eff} = 6085\pm 78$ K, a radius $R_{\thinstar} = 1.705^{+0.066}_{-0.064}$ $\mathrm{R_\odot}$ and a mass $M_\star = 1.33 \pm 0.008$~M$_\odot$. With a mass close to the hydrogen-burning minimum mass, TOI-2155\,b lies at the boundary between brown dwarfs and low-mass stars. Its measured mass, radius, and density place it in a transitional region, where distinguishing between a massive brown dwarf and a very low-mass star is not straightforward. TOI-2155\,b therefore provides a valuable benchmark for testing evolutionary models of stellar and substellar structure near the hydrogen-burning limit.

astro-ph.EP↗

arXiv2026

Segre Varieties and Desarguesian Spreads

Let $\mathrm{PG}(n-1,q)$ denote the $(n-1)$-dimensional projective space over $\mathbb{F}_q$. We investigate the intersection of two Desarguesian $(h-1)$-spreads of $\mathrm{PG}(kh-1,q)$ and show that it is determined by a subgeometry over a suitable extension field. Our approach combines a characterization of subsets of points of $\mathrm{PG}(k-1,q^h)$ closed under $q$-order subgeometries with a matrix model for Desarguesian spreads based on Moore matrices. This leads naturally to the notion of generalized Segre varieties $\mathcal S^r_{kr-1,h-1}(q)$ and a geometric description of their maximal subspaces. As a main application, we prove that if two distinct Desarguesian $(h-1)$-spreads of $\mathrm{PG}(kh-1,q)$ contain a common pseudo-arc of size $k+1$, then their intersection is precisely the system $\mathcal R^r_{h,q}$ of $(h-1)$-dimensional subspaces of $\mathcal S^r_{kr-1,h-1}(q)$, for some proper divisor $r$ of $h$.

math.CO↗

arXiv2026

An infinite family of non-extendable MRD codes

In the realm of rank-metric codes, Maximum Rank Distance (MRD) codes are optimal algebraic structures attaining the Singleton-like bound. A major open problem in this field is determining whether an MRD code can be extended to a longer one while preserving its optimality. This work investigates $\mathbb{F}_{q^m}$-linear MRD codes that are non-extendable but do not attain the maximum possible length. Geometrically, these correspond to scattered subspaces with respect to hyperplanes that are maximal with respect to inclusion but not of maximum dimension. By exploiting this geometric connection, we introduce the first infinite family of non-extendable $[4,2,3]_{q^5/q}$ MRD codes. Furthermore, we prove that these codes are self-dual up to equivalence.

cs.IT↗

arXiv2025

Zeros of special polynomials and their impact on a class of APN functions

In 2021, Calderini et al. introduced a construction for APN functions on $\mathbb{F}_{2^{2m}}$ in bivariate form $$ f(x,y)=\big(xy,\, x^{2^r+1} + x^{2^{r+m/2}} y^{2^{m/2}} + bxy^{2^r} + cy^{2^r+1}\big),\quad r < m/2,\quad \gcd(r, m) = 1. $$ They showed that this family exists provided the existence of a polynomial $$ P_{c,b}(X)=(cX^{2^r +1} + b X^{2^r}+1)^{2^{m/2}+1}+X^{2^{m/2}+1}, $$ with no zeros in $\mathbb{F}_{2^{2m}}$. For $m\le 6$ it was shown that we can have APN functions belonging to this family. However, up to now, no construction of such polynomials is known for $m\ge 8$. In this work we provide a non-existence result of such functions whenever $r<m/8-1$, by application of techniques from algebraic varieties over finite fields. In particular, for $r=1$ we have that the construction of Calderini et al. cannot provide an APN function for $m\ge 8$.

math.NT↗

arXiv2025

A lower bound on the minimum weight of some geometric codes

The $p$-ary code associated with the incidence structure of points and $t$-spaces in a projective space $\mathrm{PG}(m,q)$, where $q=p^h$, is the $\mathbb{F}_p$-subspace generated by the incidence vectors of the blocks of this design. The dual of this code consists of all vectors orthogonal to every codeword of the original code. In contrast to the codes derived from point-subspace incidences, the minimum weight of the corresponding dual codes is generally unknown, which makes the problem more challenging. In 2008 Lavrauw, Storme and Van de Voorde proved the following reduction: the minimum weight of the dual of the code derived from point and $t$-space incidences in $\mathrm{PG}(m,q)$ is the same as the minimum weight of the dual of the code derived from point and line incidences in $\mathrm{PG}(m-t+1,q)$. After a series of works by Delsarte (1970), Assmus and Key (1992), Calkin, Key and De Resmini (1999), the best known lower bound for the case of point-line incidences was established in [B. Bagchi and P. Inamdar: Projective geometric codes, J. Combin. Theory Ser. A, 99(1) (2002), 128-142]. The problem of determining the minimum weight of these codes admits a natural geometric interpretation in terms of multisets of points in a projective space which meet each line in $0$ modulo $p$ points. In this paper, by adopting this geometrical perspective and exploiting certain polynomial techniques from [S. Ball, A. Blokhuis, A. Gács, P. Sziklai, Zs. Weiner: On linear codes whose weights and length have a common divisor, Adv. Math., 211 (2007), 94-104], we prove a substantial improvement of the Bagchi-Inamdar bound in the case where $h>1$ and $m, p >2$.

math.CO↗

arXiv2025

Long QMDS additive code

We investigate additive codes, defined as $\mathbb{F}_q$-linear subspaces $C \subseteq \mathbb{F}_{q^h}^n$ of length $n$ and dimension $r$ over $\mathbb{F}_q$. An additive code is said to be of type $[n, r/h, d]_q^h$, where $d$ denotes the minimum Hamming distance and the normalized dimension $r/h$ may be fractional. A central object of interest is the class of quasi-MDS (QMDS) codes, those additive codes achieving the generalized Singleton bound: $$ d = n - \left\lceil \frac{r}{h} \right\rceil + 1. $$ In this work, we construct explicit families of additive QMDS codes whose lengths exceed those of the best-known $\mathbb{F}_{q^h}$-linear MDS codes which is $q^h+1$, and we will call these types of codes ``Long'' . By leveraging $\mathbb{F}_q$-linearity and geometric tools like partial spreads and dimensional dual arcs, we show that additive structures allow longer codes without sacrificing optimality in distance. We also examine dual codes and give conditions under which the QMDS property is preserved under duality.

math.CO↗

arXiv2025

Migration and Evolution of giant ExoPlanets (MEEP) II: Super-Jupiters and Lithium-rich Host Stars

Although hot Jupiters were the first exoplanets discovered orbiting main sequence stars, the dominant mechanisms through which they form and evolve are not known. To address the questions surrounding their origins, the Migration and Evolution of giant ExoPlanets (MEEP) survey aims to create a complete, magnitude-limited ($G<$12.5) sample of hot Jupiters that can be used to constrain the frequency of different migration pathways. NASA's Transiting Exoplanet Survey Satellite provides the unique combination of sky-coverage and photometric precision to achieve this goal, which will likely be a key result of the mission. In this second installment of the MEEP survey, we reanalyze one benchmark hot Jupiter system, TOI-4138, and discover four additional super-Jupiters which are each more than five times as massive as Jupiter: TOI-4773 b, TOI-5261 b, TOI-5350 b, and TOI-6420 b. One of these planets, TOI-5261 b, is 11.49 times the mass of Jupiter, nearly massive enough to ignite deuterium fusion, and has an eccentric ($e = 0.1585$) orbit. TOI-4138, TOI-4773, TOI-5350, and TOI-6420 each have lithium absorption features in their spectra. TOI-4138 is an F-type subgiant with a lithium equivalent width of $120. \pm 13$ mÅ, which is $\sim 4.5σ$ larger than the median lithium equivalent width of a control sample of 1381 similar stars, making TOI-4138 a compelling candidate for planetary engulfment.

astro-ph.EP↗

arXiv2025

Linear rank-metric intersecting codes

In this paper we introduce and investigate rank-metric intersecting codes, a new class of linear codes in the rank-metric context, inspired by the well-studied notion of intersecting codes in the Hamming metric. A rank-metric code is said to be intersecting if any two nonzero codewords have supports intersecting non trivially. We explore this class from both a coding-theoretic and geometric perspective, highlighting its relationship with minimal codes, MRD codes, and Hamming-metric intersecting codes. We derive structural properties, sufficient conditions based on minimum distance, and geometric characterizations in terms of 2-spannable $q$-systems. We establish upper and lower bounds on code parameters and show some constructions, which leave a range of unexplored parameters. Finally, we connect rank-intersecting codes to other combinatorial structures such as $(2,1)$-separating systems and frameproof codes.

math.CO↗

arXiv2025

Towards the classification of scattered binomials

Let $ q $ be a prime power and $ n $ an integer. An $ \mathbb{F}_q $-linearized polynomial $ f $ is said to be scattered if it satisfies the condition that for all $ x, y \in \mathbb{F}_q^n \setminus \{ 0 \} $, whenever $ \frac{f(x)}{x} = \frac{f(y)}{y} $, it follows that $ \frac{x}{y} \in \mathbb{F}_q $. In this paper, we focus on scattered binomials. Two families of scattered binomials are currently known: the one from Lunardon and Polverino (LP), given by $f(x) = δx^{q^s} + x^{q^{n-s}},$ and the one from Csajbók, Marino, Polverino, and Zanella (CMPZ), given by $f(x) = δx^{q^s} + x^{q^{s + n/2}},$ where $ n = 6 $ or $ n = 8 $. Using algebraic varieties as a tool, we prove some necessary conditions for a binomial to be scattered. As a corollary, we obtain that when $ q $ is sufficiently large and $ n $ is prime, a binomial is scattered if and only if it is of the form (LP). Moreover we obtain a complete classification of scattered binomial in $\Fn$ when $n\leq8$ and $q$ is large enough.

math.CO↗

arXiv2024

A Fourth Planet in the Kepler-51 System Revealed by Transit Timing Variations

Kepler-51 is a $\lesssim 1\,\mathrm{Gyr}$-old Sun-like star hosting three transiting planets with radii $\approx 6$-$9\,R_\oplus$ and orbital periods $\approx 45$-$130\,\mathrm{days}$. Transit timing variations (TTVs) measured with past Kepler and Hubble Space Telescope (HST) observations have been successfully modeled by considering gravitational interactions between the three transiting planets, yielding low masses and low mean densities ($\lesssim 0.1\,\mathrm{g/cm^3}$) for all three planets. However, the transit time of the outermost transiting planet Kepler-51d recently measured by the James Webb Space Telescope (JWST) 10 years after the Kepler observations is significantly discrepant from the prediction made by the three-planet TTV model, which we confirmed with ground-based and follow-up HST observations. We show that the departure from the three-planet model is explained by including a fourth outer planet, Kepler-51e, in the TTV model. A wide range of masses ($\lesssim M_\mathrm{Jup}$) and orbital periods ($\lesssim 10\,\mathrm{yr}$) are possible for Kepler-51e. Nevertheless, all the coplanar solutions found from our brute-force search imply masses $\lesssim 10\,M_\oplus$ for the inner transiting planets. Thus their densities remain low, though with larger uncertainties than previously estimated. Unlike other possible solutions, the one in which Kepler-51e is around the $2:1$ mean motion resonance with Kepler-51d implies low orbital eccentricities ($\lesssim 0.05$) and comparable masses ($\sim 5\,M_\oplus$) for all four planets, as is seen in other compact multi-planet systems. This work demonstrates the importance of long-term follow-up of TTV systems for probing longer period planets in a system.

astro-ph.EP↗

arXiv2024

Scattered trinomials of $\mathbb{F}_{q^6}[X]$ in even characteristic

In recent years, several families of scattered polynomials have been investigated in the literature. However, most of them only exist in odd characteristic. In [B. Csajbók, G. Marino and F. Zullo: New maximum scattered linear sets of the projective line, Finite Fields Appl. 54 (2018), 133-150; G. Marino, M. Montanucci and F. Zullo: MRD-codes arising from the trinomial $x^q+x^{q^3}+cx^{q^5}\in\mathbb{F}_{q^6}[x]$, Linear Algebra Appl. 591 (2020), 99-114], the authors proved that the trinomial $f_c(X)=X^{q}+X^{q^{3}}+cX^{q^{5}}$ of $\mathbb{F}_{q^6}[X]$ is scattered under the assumptions that $q$ is odd and $c^2+c=1$. They also explicitly observed that this is false when $q$ is even. In this paper, we provide a different set of conditions on $c$ for which this trinomial is scattered in the case of even $q$. Using tools of algebraic geometry in positive characteristic, we show that when $q$ is even and sufficiently large, there are roughly $q^3$ elements $c \in \mathbb{F}_{q^6}$ such that $f_{c}(X)$ is scattered. Also, we prove that the corresponding MRD-codes and $\mathbb{F}_q$-linear sets of $\mathrm{PG}(1,q^6)$ are not equivalent to the previously known ones.

math.CO↗

arXiv2024

A new infinite family of maximum $h$-scattered $\mathbb{F}_q$-subspaces of $V(m(h+1),q^n)$ and associated MRD codes

The exploration of linear subspaces, particularly scattered subspaces, has garnered considerable attention across diverse mathematical disciplines in recent years, notably within finite geometries and coding theory. Scattered subspaces play a pivotal role in analyzing various geometric structures such as blocking sets, two-intersection sets, complete arcs, caps in affine and projective spaces over finite fields and rank metric codes. This paper introduces a new infinite family of $h$-subspaces, along with their associated MRD codes. Additionally, it addresses the task of determining the generalized weights of these codes. Notably, we demonstrate that these MRD codes exhibit some larger generalized weights compared to those previously identified.

math.CO↗

arXiv2024

Dynamical Architectures of S-type Transiting Planets in Binaries I: Target Selection using Hipparcos and Gaia proper motion anomalies

The effect of stellar multiplicity on planetary architecture and orbital dynamics provides an important context for exoplanet demographics. We present a volume-limited catalog up to 300 pc of 66 stars hosting planets and planet candidates from Kepler, K2 and TESS with significant Hipparcos-Gaia proper motion anomalies, which indicate the presence of companions. We assess the reliability of each transiting planet candidate using ground-based follow-up observations, and find that the TESS Objects of Interest (TOIs) with significant proper motion anomalies show nearly four times more false positives due to Eclipsing Binaries compared to TOIs with marginal proper motion anomalies. In addition, we find tentative evidence that orbital periods of planets orbiting TOIs with significant proper motion anomalies are shorter than those orbiting TOIs without significant proper motion anomalies, consistent with the scenario that stellar companions can truncate planet-forming disks. Furthermore, TOIs with significant proper motion anomalies exhibit lower Gaia differential velocities in comparison to field stars with significant proper motion anomalies, suggesting that planets are more likely to form in binary systems with low-mass substellar companions or stellar companions at wider separation. Finally, we characterize the three-dimensional architecture of LTT 1445 ABC using radial velocities, absolute astrometry from Gaia and Hipparcos, and relative astrometry from imaging. Our analysis reveals that LTT 1445 is a nearly flat system, with a mutual inclination of 2.88 deg between the orbit of BC around A and that of C around B. The coplanarity may explain why multiple planets around LTT 1445 A survive in the dynamically hostile environment of this system.

astro-ph.EP↗

arXiv2024

A new family of $2$-scattered subspaces and related MRD codes

Scattered subspaces and $h$-scattered subspaces have been extensively studied in recent decades for both theoretical purposes and their connections to various applications. While numerous constructions of scattered subspaces exist, relatively few are known about $h$-scattered subspaces with $h\geq2$. In this paper, we establish the existence of maximum $2$-scattered $\F_q$-subspaces in $V(r,q^6)$ whenever $r\geq 3$, $r\ne 5$, and $q$ is an odd power of $2$. Additionally, we explore the corresponding MRD codes.

math.CO↗

arXiv2024

Short rank-metric codes and scattered subspaces

By exploiting the connection between scattered $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^3$ and minimal non degenerate $3$-dimensional rank metric codes of $\mathbb{F}_{q^m}^{n}$, $n \geq m+2$, described in [2], we will exhibit a new class of codes with parameters $[m+2,3,m-2]_{q^m/q}$ for infinite values of $q$ and $m \geq 5$ odd. Moreover, by studying the geometric structures of these scattered subspaces, we determine the rank weight distribution of the associated codes.

cs.IT↗