Automorphism groups of Gabidulin-like codes
Information Theory
2016-04-01 v1 Group Theory
math.IT
Representation Theory
Abstract
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.
Cite
@article{arxiv.1603.09565,
title = {Automorphism groups of Gabidulin-like codes},
author = {Dirk Liebhold and Gabriele Nebe},
journal= {arXiv preprint arXiv:1603.09565},
year = {2016}
}