Divisible Linear Rank Metric Codes
- Resource Type
- Periodical
- Authors
- Polverino, O.; Santonastaso, P.; Sheekey, J.; Zullo, F.
- Source
- IEEE Transactions on Information Theory IEEE Trans. Inform. Theory Information Theory, IEEE Transactions on. 69(7):4528-4536 Jul, 2023
- Subject
- Communication, Networking and Broadcast Technologies
Signal Processing and Analysis
Measurement
Codes
Codecs
Linearity
Quantum computing
Poles and towers
Mathematics
Divisible codes
rank metric codes
function over finite fields
idealizer
linearized polynomial
- Language
- ISSN
- 0018-9448
1557-9654
A subspace of matrices in ${\mathbb F}_{q^{e}}^{m\times n}$ can be naturally embedded as a subspace of matrices in ${\mathbb F}_{q}^{em\times en}$ 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.