A Fast Matrix Decoding Algorithm for Rank-Error-Correcting Codes

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.