A subspace of matrices in Fm×n qe can be naturally embedded as a subspace of matrices in Fem×en q with the property that the rank of any of its matrix is a multiple of e. It is quite natural to ask whether or not all subspaces of matrices with such a property arise from a subspace of matrices over a larger field. In this paper we explore this question, which corresponds to studying divisible codes in the rank metric. We determine some cases for which this question holds true, and describe counterexamples by constructing subspaces with this property which do not arise from a subspace of matrices over a larger field.
Divisible linear rank metric codes
Polverino O.;Santonastaso P.;Zullo F.
2023
Abstract
A subspace of matrices in Fm×n qe can be naturally embedded as a subspace of matrices in Fem×en q with the property that the rank of any of its matrix is a multiple of e. It is quite natural to ask whether or not all subspaces of matrices with such a property arise from a subspace of matrices over a larger field. In this paper we explore this question, which corresponds to studying divisible codes in the rank metric. We determine some cases for which this question holds true, and describe counterexamples by constructing subspaces with this property which do not arise from a subspace of matrices over a larger field.File in questo prodotto:
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