Non-minimum tensor rank Gabidulin codes
| Autor: | Bartoli, D., Zini, G., Zullo, F. |
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| Přispěvatelé: | Bartoli, D., Zini, G., Zullo, F. |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Numerical Analysis Algebra and Number Theory Information Theory (cs.IT) Delsarte-Gabidulin code Computer Science - Information Theory MRD codes Minimal tensor rank Rank metric codes Tensor rank MRD code FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Combinatorics (math.CO) Geometry and Topology Rank metric code Computer Science::Information Theory |
| Popis: | The tensor rank of some Gabidulin codes of small dimension is investigated. In particular, we determine the tensor rank of any rank metric code equivalent to an $8$-dimensional $\mathbb{F}_q$-linear generalized Gabidulin code in $\mathbb{F}_{q}^{4\times4}$. This shows that such a code is never minimum tensor rank. In this way, we detect the first infinite family of Gabidulin codes which are not minimum tensor rank. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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