Valued rank-metric codes

Journal of Algebra and Its Applications, vol. 24

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.

Authors 3

1. Yassine El Maazouz Aachen Chair of Algebra and Number Theory

   RWTH Aachen University

   Affiliation as printed

   Chair of Algebra and Number Theory, RWTH Aachen University, Pontdriesch 14/16, Office 110, D-52056 Aachen, Germany

2. Marvin Anas Hahn

   Trinity College Dublin

   Affiliation as printed

   School of Mathematics, Trinity College Dublin, 17 Westland Row, Dublin 2, Ireland

3. Mima Stanojkovski

   University of Trento

   Affiliation as printed

   Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38123 Povo di Trento (TN), Italy