scholarly journals List-decoding of subspace codes and rank-metric codes up to Singleton bound

2012 ◽  
Author(s):  
Hessam Mahdavifar ◽  
Alexander Vardy
Keyword(s):  
List Decoding ◽  
Subspace Codes ◽  
Rank Metric ◽  
Singleton Bound ◽  
Rank Metric Codes

scholarly journals Subspace codes from Ferrers diagrams

2016 ◽  
Vol 16 (07) ◽  
pp. 1750131 ◽  
Author(s):  
Elisa Gorla ◽  
Alberto Ravagnani
Keyword(s):  
Algebraic Geometry ◽  
Lower Bound ◽  
Full Rank ◽  
Sharp Bound ◽  
Closed Field ◽  
Subspace Codes ◽  
Rank Metric ◽  
Rank Metric Codes ◽  
The Given ◽  
Sharp Lower Bound

In this paper, we survey the main known constructions of Ferrers diagram rank-metric codes, and establish new results on a related conjecture by Etzion and Silberstein. We also give a sharp lower bound on the dimension of linear rank-metric anticodes with a given profile. Combining our results with the multilevel construction, we produce examples of subspace codes with the largest known cardinality for the given parameters. We also apply results from algebraic geometry to the study of the analogous problem over an algebraically closed field, proving that the bound by Etzion and Silberstein can be improved in this case, and providing a sharp bound for full-rank matrices.

On interleaved rank metric codes

2020 ◽  
Author(s):  
Vladimir Sidorenko ◽  
Wenhui Li ◽  
Gerhard Kramer
Keyword(s):  
Rank Metric ◽  
Rank Metric Codes

Bounds on subspace codes based on totally isotropic subspace in symplectic spaces and extended symplectic spaces

2019 ◽  
Vol 12 (05) ◽  
pp. 1950069
Author(s):  
Mahdieh Hakimi Poroch
Keyword(s):  
Sphere Packing ◽  
Symplectic Space ◽  
Isotropic Subspace ◽  
Subspace Codes ◽  
Singleton Bound ◽  
Symplectic Spaces ◽  
Isotropic Subspaces ◽  
Totally Isotropic Subspace ◽  
Totally Isotropic Subspaces

In this paper, we propose the Sphere-packing bound, Singleton bound and Gilbert–Varshamov bound on the subspace codes [Formula: see text] based on totally isotropic subspaces in symplectic space [Formula: see text] and on the subspace codes [Formula: see text] based on totally isotropic subspace in extended symplectic space [Formula: see text].

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