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Subspace Codes based on Graph Matchings, Ferrers Diagrams and Pending Blocks (1404.6723v2)
Published 27 Apr 2014 in cs.IT and math.IT
Abstract: This paper provides new constructions and lower bounds for subspace codes, using Ferrers diagram rank-metric codes from matchings of the complete graph and pending blocks. We present different constructions for constant dimension codes with minimum injection distance $2$ or $k-1$, where $k$ is the constant dimension. Furthermore, we present a construction of new codes from old codes for any minimum distance. Then we construct non-constant dimension codes from these codes. The examples of codes obtained by these constructions are the largest known codes for the given parameters.