Subspace Codes Based on Graph Matchings, Ferrers Diagrams, and Pending Blocks

Natalia Silberstein; Anna Lena Trautmann

doi:10.1109/TIT.2015.2435743

Subspace Codes Based on Graph Matchings, Ferrers Diagrams, and Pending Blocks

Natalia Silberstein, Anna Lena Trautmann

Research output: Contribution to journal › Article › peer-review

53 Scopus citations

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 nonconstant dimension codes from these codes. Some examples of codes obtained by these constructions are the largest known codes for the given parameters.

Original language	English
Article number	7110586
Pages (from-to)	3937-3953
Number of pages	17
Journal	IEEE Transactions on Information Theory
Volume	61
Issue number	7
DOIs	https://doi.org/10.1109/TIT.2015.2435743
State	Published - 1 Jul 2015
Externally published	Yes

Keywords

Constant dimension codes
Ferrers diagram rank-metric codes
Grassmannian
graph matchings
subspace codes

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2015.2435743

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title = "Subspace Codes Based on Graph Matchings, Ferrers Diagrams, and Pending Blocks",

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 nonconstant dimension codes from these codes. Some examples of codes obtained by these constructions are the largest known codes for the given parameters.",

keywords = "Constant dimension codes, Ferrers diagram rank-metric codes, Grassmannian, graph matchings, subspace codes",

author = "Natalia Silberstein and Trautmann, {Anna Lena}",

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AU - Trautmann, Anna Lena

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N2 - 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 nonconstant dimension codes from these codes. Some examples of codes obtained by these constructions are the largest known codes for the given parameters.

AB - 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 nonconstant dimension codes from these codes. Some examples of codes obtained by these constructions are the largest known codes for the given parameters.

KW - Constant dimension codes

KW - Ferrers diagram rank-metric codes

KW - Grassmannian

KW - graph matchings

KW - subspace codes

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ER -

Subspace Codes Based on Graph Matchings, Ferrers Diagrams, and Pending Blocks

Abstract

Keywords

ASJC Scopus subject areas

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