Error and erasure correcting algorithms for rank codes

Authors:
Ernst M. Gabidulin;Nina I. Pilipchuk
Affiliations:
Moscow Institute of Physics and Technology, State University, Dolgoprudny, Russia 141700;Moscow Institute of Physics and Technology, State University, Dolgoprudny, Russia 141700
Venue:
Designs, Codes and Cryptography
Year:
2008

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Abstract

In this paper, transmitted signals are considered as square matrices of the Maximum rank distance (MRD) (n, k, d)-codes. A new composed decoding algorithm is proposed to correct simultaneously rank errors and rank erasures. If the rank of errors and erasures is not greater than the Singleton bound, then the algorithm gives always the correct decision. If it is not a case, then the algorithm gives still the correct solution in many cases but some times the unique solution may not exist.