Valued rank-metric codes
Number Theory
2023-10-16 v2 Information Theory
Combinatorics
math.IT
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.
Keywords
Cite
@article{arxiv.2104.03216,
title = {Valued rank-metric codes},
author = {Yassine El Maazouz and Marvin Anas Hahn and Alessandro Neri and Mima Stanojkovski},
journal= {arXiv preprint arXiv:2104.03216},
year = {2023}
}
Comments
31 pages