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arxiv 2104.03216 v2 pith:LTOBF6D5 submitted 2021-04-07 math.NT cs.ITmath.COmath.IT

Valued rank-metric codes

Yassine El Maazouz , Marvin Anas Hahn , Alessandro Neri , Mima Stanojkovski This is my paper
classification math.NT cs.ITmath.COmath.IT
keywords codesrank-metricdimensionfieldsringsvaluedadditionallyalgebras
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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.

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