Zobrazeno 1 - 10
of 918
pro vyhledávání: '"NERI, Alessandro"'
There are many similarities between the theories of matroids and $q$-matroids. However, when dealing with the direct sum of $q$-matroids many differences arise. Most notably, it has recently been shown that the direct sum of representable $q$-matroid
Externí odkaz:
http://arxiv.org/abs/2408.00630
We derive eigenvalue bounds for the $t$-distance chromatic number of a graph, which is a generalization of the classical chromatic number. We apply such bounds to hypercube graphs, providing alternative spectral proofs for results by Ngo, Du and Grah
Externí odkaz:
http://arxiv.org/abs/2404.14839
Autor:
Neri, Alessandro, Stanojkovski, Mima
Ferrers diagram rank-metric codes were introduced by Etzion and Silberstein in 2009. In their work, they proposed a conjecture on the largest dimension of a space of matrices over a finite field whose nonzero elements are supported on a given Ferrers
Externí odkaz:
http://arxiv.org/abs/2306.16407
A strong blocking set in a finite projective space is a set of points that intersects each hyperplane in a spanning set. We provide a new graph theoretic construction of such sets: combining constant-degree expanders with asymptotically good codes, w
Externí odkaz:
http://arxiv.org/abs/2305.15297
In this paper we extend the study of linear spaces of upper triangular matrices endowed with the flag-rank metric. Such metric spaces are isometric to certain spaces of degenerate flags and have been suggested as suitable framework for network coding
Externí odkaz:
http://arxiv.org/abs/2303.16653
Autor:
Bik, Arthur, Neri, Alessandro
Over fields of characteristic unequal to $2$, we can identify symmetric matrices with homogeneous polynomials of degree $2$. This allows us to view symmetric rank-metric codes as living inside the space of such polynomials. In this paper, we generali
Externí odkaz:
http://arxiv.org/abs/2303.06745
Strong blocking sets, introduced first in 2011 in connection with saturating sets, have recently gained a lot of attention due to their correspondence with minimal codes. In this paper, we dig into the geometry of the concatenation method, introducin
Externí odkaz:
http://arxiv.org/abs/2301.09590
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
Externí odkaz:
http://arxiv.org/abs/2211.11477
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 th
Externí odkaz:
http://arxiv.org/abs/2209.02586
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-m
Externí odkaz:
http://arxiv.org/abs/2204.11791