Subspace codes from Ferrers diagrams
Elisa Gorla, Alberto Ravagnani
TL;DR
This paper introduces new Ferrers diagram rank metric code constructions that achieve maximal dimension, proves cases of a conjecture, and produces subspace codes with record sizes using multilevel methods.
Contribution
It provides novel constructions of Ferrers diagram rank metric codes, proves several cases of a conjecture, and establishes bounds leading to large subspace codes.
Findings
Achieved the largest possible dimension for Ferrers diagram rank metric codes.
Proved several cases of a conjecture by Etzion and Silberstein.
Produced subspace codes with the largest known cardinality for given parameters.
Abstract
In this paper we give new constructions of Ferrer diagram rank metric codes, which achieve the largest possible dimension. In particular, we prove several cases of a conjecture by T. Etzion and N. Silberstein. We also establish a sharp lower bound on the dimension of linear rank metric anticodes with a given profile. Combining our results with the multilevel construction, we produce examples of subspace codes with the largest known cardinality for the given parameters.
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