A fast matrix decoding algorithm for rank-error-correcting codes

EM Gabidulin - Workshop on Algebraic Coding, 1991 - Springer
EM Gabidulin
Workshop on Algebraic Coding, 1991Springer
The so-called term-rank and rank metrics and appropriate codes were introduced and
investigated in [1–7]. These metrics and codes can be used for correcting array errors in a
set of parallel channels, for scrambling in channels with burst errors, as basic codes in
McEliece public key cryptosystem [8], etc. For codes with maximal rank distance (MRD
codes) there exists a fast decoding algorithm based on Euclid's Division Algorithm in some
non-commutative ring [6]. In this paper a new construction of MRD codes is given and a new …
Abstract
The so-called term-rank and rank metrics and appropriate codes were introduced and investigated in [1 –7]. These metrics and codes can be used for correcting array errors in a set of parallel channels, for scrambling in channels with burst errors, as basic codes in McEliece public key cryptosystem [8], etc. For codes with maximal rank distance (MRD codes) there exists a fast decoding algorithm based on Euclid's Division Algorithm in some non-commutative ring [6]. In this paper a new construction of MRD codes is given and a new fast matrix decoding algorithm is proposed which generalizes Peterson's algorithm [9] for BCH codes.
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