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On the Non ‐ Existence of Perfect Codes with Rank Distance
Author(s) -
Chen Kefei
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19961820106
Subject(s) - mathematics , rank (graph theory) , hamming bound , block code , coding theory , minimum distance , discrete mathematics , linear code , combinatorics , algorithm , decoding methods
Theory of codes with rank distance was introduced in 1985, which can be applied to crisscross error correction and also used to build some cryptographical schemes. We know that the existence of perfect codes is an interesting topic in coding theory; as a new type of codes, we consider the existence of the perfect rank distance codes and prove that there are no non‐trivial perfect codes with rank metric.