Constructions of optimal Ferrers diagram rank metric codes
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Subspace codes and constant dimension codes have become a widely investigated research topic due to their significance to error control in random linear network coding. Rank metric codes in Ferrers diagrams can be used to construct good subspace codes and constant dimension codes. In this paper, three constructions of Ferrers diagram rank metric codes are presented. The first two constructions are based on subcodes of maximum rank distance codes, and the last one generates new codes from known Ferrers diagram rank metric codes. Each of these constructions produces optimal codes with different diagrams and parameters for which no optimal construction was known before.
KeywordsFerrers diagram Rank metric code Gabidulin code Subspace code Constant dimension code
Mathematics Subject Classification15A03 15A99 15B99
The authors express their gratitude to the anonymous reviewers for their detailed and constructive comments which are very helpful to the improvement of this paper, and to Prof. Tuvi Etzion, the Associate Editor, for his insightful advice and excellent editorial job.
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