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(4x4). 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. (c) 2022 Elsevier Inc. All rights reserved.
Non-minimum tensor rank Gabidulin codes
Bartoli, D;
2022
Abstract
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(4x4). 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. (c) 2022 Elsevier Inc. All rights reserved.File in questo prodotto:
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