Title :
Rank metric and Gabidulin codes in characteristic zero
Author :
Augot, Daniel ; Loidreau, Pierre ; Robert, Grepl
Author_Institution :
INRIA Saclay-Ile-de-France, Ecole Polytech., Palaiseau, France
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.
Keywords :
Galois fields; codes; decoding; polynomials; Frobenius automorphism; Gabidulin code; Galois group; characteristic zero field; polynomial-time decoding algorithm; rank metric code; Complexity theory; Decoding; Encoding; Measurement; Polynomials; Space-time codes; Gabidulin codes; Ore rings; Space-time coding; algebraic decoding; number fields; rank metric; skew polynomials;
Conference_Titel :
Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on
Conference_Location :
Istanbul
DOI :
10.1109/ISIT.2013.6620278
