Archiv der Mathematik

, Volume 107, Issue 4, pp 355–366 | Cite as

Automorphism groups of Gabidulin-like codes

  • Dirk Liebhold
  • Gabriele Nebe


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.

Mathematics Subject Classification

94B05 20B25 


Rank metric codes MRD codes Automorphism group Gabidulin-like code 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Lehrstuhl D für MathematikRWTH Aachen UniversityAachenGermany

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