Rank metric and Gabidulin codes in characteristic zero

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 w...

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Bibliographic Details
Main Authors: Augot, Daniel, Loidreau, Pierre, Robert, Gwezheneg
Format: Conference Proceeding
Language:English
Subjects:
algebraic decoding
Complexity theory
Decoding
Encoding
Gabidulin codes
Measurement
number fields
Ore rings
Polynomials
rank metric
skew polynomials
Space-time codes
Space-time coding
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Summary: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.
ISSN:2157-8095
2157-8117
DOI:10.1109/ISIT.2013.6620278