Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.  characterise the K-linear codes that are Gabidulin-like codes and determine their rank-metric automorphism group.
['Dirk Liebhold', 'Gabriele Nebe']
I am writing a research paper on a idea Automorphism groups of Gabidulin-like codes
[{"from": "human", "value": "I am writing a research paper on a idea Automorphism groups of Gabidulin-like codes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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.  characterise the K-linear codes that are Gabidulin-like codes and determine their rank-metric automorphism group."}]