Rank metric and Gabidulin codes in characteristic zero
Information Theory
2013-05-20 v1 math.IT
Abstract
We transpose the theory of rank metric and Gabidulin codes to the case of fields of characteristic zero. The Frobenius automorphism is then replaced by any element of the Galois group. We derive some conditions on the automorphism to be able to easily transpose the results obtained by Gabidulin as well and a classical polynomial-time decoding algorithm. We also provide various definitions for the rank-metric.
Cite
@article{arxiv.1305.4047,
title = {Rank metric and Gabidulin codes in characteristic zero},
author = {Gwezheneg Robert and Pierre Loidreau and Daniel Augot},
journal= {arXiv preprint arXiv:1305.4047},
year = {2013}
}