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

Author

Silberstein, Natalia ; Trautmann, Anna-Lena

Author_Institution

Dept. of Comput. Sci., Technion - Israel Inst. of Technol., Haifa, Israel

Volume

61

Issue

7

fYear

2015

fDate

Jul-15

Firstpage

3937

Lastpage

3953

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

codes; graph theory; Ferrers diagram rank metric codes; constant dimension; constant dimension codes; graph matchings; injection distance; old codes; pending blocks; subspace codes; Electronic mail; Error correction codes; Frequency modulation; Generators; Hamming distance; Measurement; Upper bound; Constant dimension codes; Ferrers diagram rank-metric codes; Grassmannian; graph matchings; subspace codes;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2015.2435743

Filename

7110586