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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
10/2021

Valued rank-metric codes

Yassine El Maazouz, Marvin Anas Hahn, Alessandro Neri and Mima Stanojkovski

Abstract

In this paper, we study linear spaces of matrices defined over discretely valued fields and discuss their dimension and minimal rank drops over the associated residue fields. To this end, we take first steps into the theory of rank-metric codes over discrete valuation rings by means of skew algebras derived from Galois extensions of rings. Additionally, we model projectivizations of rank-metric codes via Mustafin varieties, which we then employ to give sufficient conditions for a decrease in the dimension.

Received:
08.04.21
Published:
08.04.21
MSC Codes:
05E14, 11T71, 94B05
Keywords:
rank-metric codes, discretely valued fields, Bruhat-Tits buildings, skew algebras, Mustafin varieties, MRD codes

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Preprint
2021 Repository Open Access
Yassine El Maazouz, Marvin Anas Hahn, Alessandro Neri and Mima Stanojkovski

Valued rank-metric codes