Abstract
Let K/k be a cyclic Galois extension of degree \({\ell}\) and \({\theta }\) a generator of Gal(K/k). For any \({v=(v_1, \ldots, v_m)\in K^{m}}\) such that v is linearly independent over k, and any \({1\leq d < m }\) the Gabidulin-like code \({\mathcal{C}(v,\theta, d) \leq k^{\ell \times m }}\) is a maximum rank distance code of dimension \({\ell d}\) over k. This construction unifies the ones available in the literature. We characterise the K-linear codes that are Gabidulin-like codes and determine their rank-metric automorphism group.
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Dedicated to Ernst-Ulrich Gekeler.
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Liebhold, D., Nebe, G. Automorphism groups of Gabidulin-like codes. Arch. Math. 107, 355–366 (2016). https://doi.org/10.1007/s00013-016-0949-4
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DOI: https://doi.org/10.1007/s00013-016-0949-4