Nuclei and automorphism groups of generalized twisted Gabidulin codes
Combinatorics
2019-04-16 v2 Information Theory
math.IT
Abstract
Generalized twisted Gabidulin codes are one of the few known families of maximum rank matrix codes over finite fields. As a subset of m by n matrices, when m=n, the automorphism group of any generalized twisted Gabidulin code has been completely determined recently. In this paper, we consider the same problem for m<n. Under certain conditions on their parameters, we determine their middle nuclei and right nuclei, which are important invariants with respect to the equivalence for rank metric codes. Furthermore, we also use them to derive necessary conditions on the automorphisms of generalized twisted Gabidulin codes.
Cite
@article{arxiv.1611.04447,
title = {Nuclei and automorphism groups of generalized twisted Gabidulin codes},
author = {Rocco Trombetti and Yue Zhou},
journal= {arXiv preprint arXiv:1611.04447},
year = {2019}
}
Comments
Compared with the previous version, typos are corrected