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Rank metric and Gabidulin codes in characteristic zero

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.
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Submitted on : Friday, May 17, 2013 - 11:40:44 AM
Last modification on : Wednesday, April 6, 2022 - 3:48:03 PM
Long-term archiving on: : Tuesday, April 4, 2017 - 7:46:13 AM


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  • HAL Id : hal-00823535, version 1


Daniel Augot, Pierre Loidreau, Gwezheneg Robert. Rank metric and Gabidulin codes in characteristic zero. ISIT 2013 IEEE International Symposium on Information Theory, Amos Lapidoth and Igal Sason and Jossy Sayir and Emre Telatar, Jul 2013, Istanbul, Turkey. ⟨hal-00823535⟩



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