Automorphism groups of Gabidulin-like codes [article]

Dirk Liebhold, Gabriele Nebe
2016 arXiv   pre-print
Let K be a cyclic Galois extension of degree f over k and T a generator of the Galois group. For any v=(v_1,... , v_m)\in K^m such that v is linearly independent over k, and any 0< d < m the Gabidulin-like code C(v, T , d) is a maximum rank distance code in the space of f times m matrices over k of dimension fd. 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.
arXiv:1603.09565v1 fatcat:uf3xib5u6rh4pjhb4inwmcqhne