arXiv subjects

Giuseppe Marino

Publications and source records attributed to Giuseppe Marino.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2023

Saturating linear sets of minimal rank

Saturating sets are combinatorial objects in projective spaces over finite fields that have been intensively investigated in the last three decades. They are related to the so-called covering problem of codes in the Hamming metric. In this paper, we consider the recently introduced linear version of such sets, which is, in turn, related to the covering problem in the rank metric. The main questions in this context are how small the rank of a saturating linear set can be and how to construct saturating linear sets of small rank. Recently, Bonini, Borello, and Byrne provided a lower bound on the rank of saturating linear sets in a given projective space, which is shown to be tight in some cases. In this paper, we provide construction of saturating linear sets meeting the lower bound and we develop a link between the saturating property and the scatteredness of linear sets. The last part of the paper is devoted to show some parameters for which the bound is not tight.

math.CO↗

arXiv2023

On the maximum field of linearity of linear sets

Let $V$ denote an $r$-dimensional $\mathbb{F}_{q^n}$-vector space. For an $m$-dimensional $\mathbb{F}_q$-subspace $U$ of $V$ assume that $\dim_q \left(\langle {\bf v}\rangle_{\mathbb{F}_{q^n}} \cap U\right) \geq 2$ for each non zero vector ${\bf v}\in U$. If $n\leq q$ then we prove the existence of an integer $1<d \mid n$ such that the set of one-dimensional $\mathbb{F}_{q^n}$-subspaces generated by non-zero vectors of $U$ is the same as the set of one-dimensional $\mathbb{F}_{q^n}$-subspaces generated by non-zero vectors of $\langle U\rangle_{\mathbb{F}_{q^d}}$. If we view $U$ as a point set of $\mathrm{AG}(r,q^n)$, it means that $U$ and $\langle U \rangle_{\mathbb{F}_{q^d}}$ determine the same set of directions. We prove a stronger statement when $n \mid m$. In terms of linear sets it means that an $\mathbb{F}_q$-linear set of $\mathrm{PG}(r-1,q^n)$ has maximum field of linearity $\mathbb{F}_q$ only if it has a point of weight one. We also present some consequences regarding the size of a linear set.

math.CO↗

arXiv2023

Identification of the Top TESS Objects of Interest for Atmospheric Characterization of Transiting Exoplanets with JWST

JWST has ushered in an era of unprecedented ability to characterize exoplanetary atmospheres. While there are over 5,000 confirmed planets, more than 4,000 TESS planet candidates are still unconfirmed and many of the best planets for atmospheric characterization may remain to be identified. We present a sample of TESS planets and planet candidates that we identify as "best-in-class" for transmission and emission spectroscopy with JWST. These targets are sorted into bins across equilibrium temperature $T_{\mathrm{eq}}$ and planetary radius $R{_\mathrm{p}}$ and are ranked by transmission and emission spectroscopy metric (TSM and ESM, respectively) within each bin. In forming our target sample, we perform cuts for expected signal size and stellar brightness, to remove sub-optimal targets for JWST. Of the 194 targets in the resulting sample, 103 are unconfirmed TESS planet candidates, also known as TESS Objects of Interest (TOIs). We perform vetting and statistical validation analyses on these 103 targets to determine which are likely planets and which are likely false positives, incorporating ground-based follow-up from the TESS Follow-up Observation Program (TFOP) to aid the vetting and validation process. We statistically validate 23 TOIs, marginally validate 33 TOIs to varying levels of confidence, deem 29 TOIs likely false positives, and leave the dispositions for 4 TOIs as inconclusive. 14 of the 103 TOIs were confirmed independently over the course of our analysis. We provide our final best-in-class sample as a community resource for future JWST proposals and observations. We intend for this work to motivate formal confirmation and mass measurements of each validated planet and encourage more detailed analysis of individual targets by the community.

astro-ph.EP↗

arXiv2022

Exceptional scattered sequences

The concept of scattered polynomials is generalized to those of exceptional scattered sequences which are shown to be the natural algebraic counterpart of $\mathbb{F}_{q^n}$-linear MRD codes. The first infinite family in the first nontrivial case is also provided and equivalence issues are considered. As a byproduct, a new infinite family of MRD codes is obtained.

math.CO↗

arXiv2022

New MRD codes from linear cutting blocking sets

Minimal rank-metric codes or, equivalently, linear cutting blocking sets are characterized in terms of the second generalized rank weight, via their connection with evasiveness properties of the associated $q$-system. Using this result, we provide the first construction of a family of $\mathbb{F}_{q^m}$-linear MRD codes of length $2m$ that are not obtained as a direct sum of two smaller MRD codes. In addition, such a family has better parameters, since its codes possess generalized rank weights strictly larger than those of the previously known MRD codes. This shows that not all the MRD codes have the same generalized rank weights, in contrast to what happens in the Hamming metric setting.

math.CO↗

arXiv2022

Evasive subspaces, generalized rank weights and near MRD codes

We revisit and extend the connections between $\mathbb{F}_{q^m}$-linear rank-metric codes and evasive $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^k$. We give a unifying framework in which we prove in an elementary way how the parameters of a rank-metric code are related to special geometric properties of the associated evasive subspace, with a particular focus on the generalized rank weights. In this way, we can also provide alternative and very short proofs of known results on scattered subspaces. We then use this simplified point of view in order to get a geometric characterization of near MRD codes and a clear bound on their maximal length. Finally we connect the theory of quasi-MRD codes with $h$-scattered subspaces of maximum dimension, extending to all the parameters sets the already known results on MRD codes.

math.CO↗

arXiv2021

TOI-2109b: An Ultrahot Gas Giant on a 16 hr Orbit

We report the discovery of an ultrahot Jupiter with an extremely short orbital period of $0.67247414\,\pm\,0.00000028$ days ($\sim$16 hr). The $1.347 \pm 0.047$ $R_{\rm Jup}$ planet, initially identified by the Transiting Exoplanet Survey Satellite (TESS) mission, orbits TOI-2109 (TIC 392476080): a $T_{\rm eff} \sim 6500$ K F-type star with a mass of $1.447 \pm 0.077$ $M_{\rm Sun}$, a radius of $1.698 \pm 0.060$ $R_{\rm Sun}$, and a rotational velocity of $v\sin i_* = 81.9 \pm 1.7$ km s$^{-1}$. The planetary nature of TOI-2109b was confirmed through radial velocity measurements, which yielded a planet mass of $5.02 \pm 0.75$ $M_{\rm Jup}$. Analysis of the Doppler shadow in spectroscopic transit observations indicates a well-aligned system, with a sky-projected obliquity of $λ= 1\overset{\circ}{.}7 \pm 1\overset{\circ}{.}7$. From the TESS full-orbit light curve, we measured a secondary eclipse depth of $731 \pm 46$ ppm, as well as phase-curve variations from the planet's longitudinal brightness modulation and ellipsoidal distortion of the host star. Combining the TESS-band occultation measurement with a $K_s$-band secondary eclipse depth ($2012 \pm 80$ ppm) derived from ground-based observations, we find that the dayside emission of TOI-2109b is consistent with a brightness temperature of $3631 \pm 69$ K, making it the second hottest exoplanet hitherto discovered. By virtue of its extreme irradiation and strong planet-star gravitational interaction, TOI-2109b is an exceptionally promising target for intensive follow-up studies using current and near-future telescope facilities to probe for orbital decay, detect tidally driven atmospheric escape, and assess the impacts of H$_2$ dissociation and recombination on the global heat transport.

astro-ph.EP↗

arXiv2021

Combining subspace codes

In the context of constant--dimension subspace codes, an important problem is to determine the largest possible size $A_q(n, d; k)$ of codes whose codewords are $k$-subspaces of $\mathbb{F}_q^n$ with minimum subspace distance $d$. Here in order to obtain improved constructions, we investigate several approaches to combine subspace codes. This allow us to present improvements on the lower bounds for constant--dimension subspace codes for many parameters, including $A_q(10, 4; 5)$, $A_q(12, 4; 4)$, $A_q(12, 6, 6)$ and $A_q(16, 4; 4)$.

math.CO↗

arXiv2021

A large family of maximum scattered linear sets of $\mathrm{PG}(1,q^n)$ and their associated MRD codes

The concept of linear set in projective spaces over finite fields was introduced by Lunardon in 1999 and it plays central roles in the study of blocking sets, semifields, rank-distance codes and etc. A linear set with the largest possible cardinality and rank is called maximum scattered. Despite two decades of study, there are only a limited number of maximum scattered linear sets of a line $\mathrm{PG}(1,q^n)$. In this paper, we provide a large family of new maximum scattered linear sets over $\mathrm{PG}(1,q^n)$ for any even $n\geq 6$ and odd $q$. In particular, the relevant family contains at least \[ \begin{cases} \left\lfloor\frac{q^t+1}{8rt}\right\rfloor,& \text{ if }t\not\equiv 2\pmod{4};\\[8pt] \left\lfloor\frac{q^t+1}{4rt(q^2+1)}\right\rfloor,& \text{ if }t\equiv 2\pmod{4}, \end{cases} \] inequivalent members for given $q=p^r$ and $n=2t>8$, where $p=\mathrm{char}(\mathbb{F}_q)$. This is a great improvement of previous results: for given $q$ and $n>8$, the number of inequivalent maximum scattered linear sets of $\mathrm{PG}(1,q^n)$ in all classes known so far, is smaller than $q^2$. Moreover, we show that there are a large number of new maximum rank-distance codes arising from the constructed linear sets.

math.CO↗

arXiv2021

TOI-1278 B: SPIRou unveils a rare Brown Dwarf Companion in Close-In Orbit around an M dwarf

We present the discovery of an $18.5\pm0.5$M$_{\rm Jup}$ brown dwarf (BD) companion to the M0V star TOI-1278. The system was first identified through a percent-deep transit in TESS photometry; further analysis showed it to be a grazing transit of a Jupiter-sized object. Radial velocity (RV) follow-up with the SPIRou near-infrared high-resolution velocimeter and spectropolarimeter in the framework of the 300-night SPIRou Legacy Survey (SLS) carried out at the Canada-France-Hawaii Telescope (CFHT) led to the detection of a Keplerian RV signal with a semi-amplitude of $2306\pm10$ m/s in phase with the 14.5-day transit period, having a slight but non-zero eccentricity. The intermediate-mass ratio ($M_\star/M_{\rm{comp}} \sim31$) is unique for having such a short separation ($0.095\pm0.001$ AU) among known M-dwarf systems. Interestingly, M dwarf-brown dwarf systems with similar mass ratios exist with separations of tens to thousands of AUs.

astro-ph.SR↗

arXiv2021

On near-MDS codes and caps

Several classes of near-MDS codes of ${\rm PG}(3,q)$ are described. They are obtained either by considering the intersection of an elliptic quadric ovoid and a Suzuki-Tits ovoid of a symplectic polar space ${\cal W}(3, q)$ or starting from the $q+1$ points of a twisted cubic of ${\rm PG}(3, q)$. As a by-product two classes of complete caps of ${\rm PG}(4,q)$ of size $2q^2-q \pm \sqrt{2q} + 2$ are exhibited.

math.CO↗

arXiv2021

Small complete caps in ${\rm PG}(4n + 1, q)$

In this paper we prove the existence of a complete cap of ${\rm PG}(4n+1, q)$ of size $2(q^{2n+1}-1)/(q-1)$, for each prime power $q>2$. It is obtained by projecting two disjoint Veronese varieties of ${\rm PG}(2n^2+3n, q)$ from a suitable $(2n^2-n-2)$-dimensional projective space. This shows that the trivial lower bound for the size of the smallest complete cap of ${\rm PG}(4n+1, q)$ is essentially sharp.

math.CO↗

arXiv2021

Evasive subspaces

Let $V$ denote an $r$-dimensional vector space over $\mathbb{F}_{q^n}$, the finite field of $q^n$ elements. Then $V$ is also an $rn$-dimension vector space over $\mathbb{F}_q$. An $\mathbb{F}_q$-subspace $U$ of $V$ is $(h,k)_q$-evasive if it meets the $h$-dimensional $\mathbb{F}_{q^n}$-subspaces of $V$ in $\mathbb{F}_q$-subspaces of dimension at most $k$. The $(1,1)_q$-evasive subspaces are known as scattered and they have been intensively studied in finite geometry, their maximum size has been proved to be $\lfloor rn/2 \rfloor$ when $rn$ is even or $n=3$. We investigate the maximum size of $(h,k)_q$-evasive subspaces, study two duality relations among them and provide various constructions. In particular, we present the first examples, for infinitely many values of $q$, of maximum scattered subspaces when $r=3$ and $n=5$. We obtain these examples in characteristics $2$, $3$ and $5$.

math.CO↗

arXiv2021

On regular systems of finite classical polar spaces

Let $\cal P$ be a finite classical polar space of rank $d$. An $m$-regular system with respect to $(k - 1)$-dimensional projective spaces of $\cal P$, $1 \le k \le d - 1$, is a set $\cal R$ of generators of $\cal P$ with the property that every $(k - 1)$-dimensional projective space of $\cal P$ lies on exactly $m$ generators of $\cal R$. Regular systems of polar spaces are investigated. Some non-existence results about certain 1-regular systems of polar spaces with low rank are proved and a procedure to obtain $m'$-regular systems from a given $m$-regular system is described. Finally, three different construction methods of regular systems w.r.t. points of various polar spaces are discussed.

math.CO↗

arXiv2020

On cutting blocking sets and their codes

Let PG$(r, q)$ be the $r$-dimensional projective space over the finite field ${\rm GF}(q)$. A set $\cal X$ of points of PG$(r, q)$ is a cutting blocking set if for each hyperplane $Π$ of PG$(r, q)$ the set $Π\cap \cal X$ spans $Π$. Cutting blocking sets give rise to saturating sets and minimal linear codes and those having size as small as possible are of particular interest. We observe that from a cutting blocking set obtained by Fancsali and Sziklai, by using a set of pairwise disjoint lines, there arises a minimal linear code whose length grows linearly with respect to its dimension. We also provide two distinct constructions: a cutting blocking set of PG$(3, q^3)$ of size $3(q+1)(q^2+1)$ as a union of three pairwise disjoint $q$-order subgeometries and a cutting blocking set of PG$(5, q)$ of size $7(q+1)$ from seven lines of a Desarguesian line spread of PG$(5, q)$. In both cases the cutting blocking sets obtained are smaller than the known ones. As a byproduct we further improve on the upper bound of the smallest size of certain saturating sets and on the minimum length of a minimal $q$-ary linear code having dimension $4$ and $6$.

math.CO↗