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math.CO2023★ 1 cited
A proof of the Etzion-Silberstein conjecture for monotone and MDS-constructible Ferrers diagrams
Alessandro Neri, Mima Stanojkovski
Ferrers diagram rank-metric codes were introduced by Etzion and Silberstein in 2009. In their work, they proposed a conjecture on the largest dimension of a space of matrices over…
math.CO2021★ 5 cited
Orders and Polytropes: Matrix Algebras from Valuations
Yassine El Maazouz, Marvin Anas Hahn, Gabriele Nebe +2
We apply tropical geometry to study matrix algebras over a field with valuation. Using the shapes of min-max convexity, known as polytropes, we revisit the graduated orders introdu…