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Theory of codes with maximum rank distance. (English. Russian original) Zbl 0585.94013
Probl. Inf. Transm. 21, 1-12 (1985); translation from Probl. Peredachi Inf. 21, No. 1, 3-16 (1985).
This paper introduces a new metric, called the “rank metric”. For this metric, a theory of codes over $$\mathrm{GF}(q^N)$$ analogous to the theory of MBD codes is formulated. The studies presented include codes with maximum rank distance, their spectrum, and encoding and decoding algorithms. Analogous to “generalized Reed-Solomon codes” an extensive class of MRD codes (maximum rank distance codes) are described.

##### MSC:
 94B05 Linear codes, general