Non-minimum tensor rank Gabidulin codes

01/20/2022

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by   Daniele Bartoli, et al.

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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 𝔽_q-linear generalized Gabidulin code in 𝔽_q^4×4. 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.