We prove that for every prime power $q$ and every integer $r\geq 3$ there exists a maximum $2$-scattered $\mathbb{F}_q$-subspace of $V(r,q^6)$, that is, a $2r$-dimensional $\mathbb{F}_q$-subspace meeting every $2$-dimensional $\mathbb{F}_{q^6}$-subspace in dimension at most $2$. Since an example in dimension three is k...
Daniele Bartoli, Francesco Ghiandoni, A. Giannoni et al.· 0 citations
The generalized packing--covering conjecture of Elimelech, Firer and Schwartz asserts that, for every linear code $\mathcal{C}$ and every admissible order $t$, the $t$-th generalized Hamming weight $d_t(\mathcal{C})$ and the $t$-th generalized covering radius $R_t(\mathcal{C})$ satisfy $d_t(\mathcal{C})\le 2R_t(\mathca...
Gianira N. Alfarano, G. Marino, Alessandro Neri et al.· 0 citations
We study Schubert subspace codes, which are constant-dimension subspace codes with prescribed intersection conditions with a fixed subspace. Our goal is to construct codes of maximum possible size in the extremal distance cases where a natural counting upper bound applies. We give two families of constructions. The fir...
Gianira N. Alfarano, Alessandro Neri, Beatrice Toesca· arXiv.org· 0 citations
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