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Generalising the Scattered Property of Subspaces

Autor: Ferdinando Zullo, Bence Csajbók, Giuseppe Marino, Olga Polverino

Let $V$ be an $r$-dimensional $\mathbb{F}_{q^n}$-vector space. We call an $\mathbb{F}_q$-subspace $U$ of $V$ $h$-scattered if $U$ meets the $h$-dimensional $\mathbb{F}_{q^n}$-subspaces of $V$ in $\mathbb{F}_q$-subspaces of dimension at most $h$. In 2

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::17456e6144a5f63a00ee49dfbad614ec
http://hdl.handle.net/11588/842640

MRD-codes arising from the trinomial xq+xq3+cxq5∈Fq6[x]

Autor: Marino, Giuseppe, Montanucci, Maria, Zullo, Ferdinando

Publikováno v: Marino, G, Montanucci, M & Zullo, F 2020, ' MRD-codes arising from the trinomial x q +x q 3 +cx q 5 ∈F q 6 [x] ', Linear Algebra and Its Applications, vol. 591, pp. 99-114 . https://doi.org/10.1016/j.laa.2020.01.004

In [10], the existence of Fq-linear MRD-codes of Fq 6×6, with dimension 12, minimum distance 5 and left idealiser isomorphic to Fq6 , defined by a trinomial of Fq6 [x], when q is odd and q≡0,±1(mod5), has been proved. In this paper we show that t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::6c7bad037e259b6c976e3de7c0460da4
http://hdl.handle.net/11591/458849

Scattered subspaces and related codes

Autor: Ferdinando Zullo, Giovanni Zini

After a seminal paper by Shekeey (Adv Math Commun 10(3):475-488, 2016), a connection between maximum h-scattered $${{\mathbb {F}}}_{q}$$ -subspaces of $$V(r,q^n)$$ and maximum rank distance (MRD) codes has been established in the extremal cases $$h=1

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6a7401d4e140c0e5ddf843fff8206753