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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1534655
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