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Designs, Codes and Cryptography

Erschienen in:

24.05.2021

Scattered subspaces and related codes

verfasst von: Giovanni Zini, Ferdinando Zullo

Erschienen in: Designs, Codes and Cryptography | Ausgabe 8/2021

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Abstract

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 \(h=1\) and \(h=r-1\). In this paper, we propose a connection for any \(h\in \{1,\ldots ,r-1\}\), extending and unifying all the previously known ones. As a consequence, we obtain examples of non-square MRD codes which are not equivalent to generalized Gabidulin or twisted Gabidulin codes. We show that, up to equivalence, MRD codes having the same parameters as the ones in our connection come from an h-scattered subspace. Also, we determine the weight distribution of codes related to the geometric counterpart of maximum h-scattered subspaces.

Vorheriger Artikel A construction for circulant type dropout designs

Nächster Artikel Security analysis of Subterranean 2.0

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Titel: Scattered subspaces and related codes
verfasst von: Giovanni Zini
Ferdinando Zullo
Publikationsdatum: 24.05.2021
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 8/2021
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-021-00891-7

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Scattered subspaces and related codes

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