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Subspace codes from Ferrers diagrams (1405.2736v2)
Published 12 May 2014 in cs.IT, math.CO, and math.IT
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.