In this paper, we study linear spaces of matrices defined over discretelyvalued fields . We take first steps into the theory ofrank-metric codes over discrete valuation rings by means of skew algebras derived from Galois extensions of rings . We modelprojectivizations of rank-metic codes via Mustafin varieties, which we then give sufficient conditions for a decrease in the dimension .

Author(s) : Yassine El Maazouz, Marvin Anas Hahn, Alessandro Neri, Mima Stanojkovski

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Keywords : codes - rank - rings - metric - -

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