Rank metric and Gabidulin codes in characteristic zero [article]

Gwezheneg Robert, Pierre Loidreau, Daniel Augot
2013 arXiv   pre-print
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.
arXiv:1305.4047v1 fatcat:by3ecimsf5cfdbquvsfljkz4gq