Theory of codes with maximum rank distance. (English. Russian original) Zbl 0585.94013

Gabidulin, È. M.

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.

Reviewer: Bal Kishan Dass (Delhi)

MSC:

94B05

Linear codes, general

Keywords:

Hamming metric; rank metric; MBD codes; spectrum; encoding and decoding algorithms