NDLI: Constant-Rank Codes and Their Connection to Constant-Dimension Codes

Content Provider	IEEE Xplore Digital Library
Author	Gadouleau, M. Zhiyuan Yan
Copyright Year	1963
Abstract	Constant-dimension codes have recently received attention due to their significance to error control in noncoherent random linear network coding. What the maximal cardinality of any constant-dimension code with finite dimension and minimum distance is and how to construct the optimal constant-dimension code (or codes) that achieves the maximal cardinality both remain open research problems. In this paper, we introduce a new approach to solving these two problems. We first establish a connection between constant-rank codes and constant-dimension codes. Via this connection, we show that optimal constant-dimension codes correspond to optimal constant-rank codes over matrices with sufficiently many rows. As such, the two aforementioned problems are equivalent to determining the maximum cardinality of constant-rank codes and to constructing optimal constant-rank codes, respectively. To this end, we then derive bounds on the maximum cardinality of a constant-rank code with a given minimum rank distance, propose explicit constructions of optimal or asymptotically optimal constant-rank codes, and establish asymptotic bounds on the maximum rate of a constant-rank code.
Sponsorship	IEEE Information Theory Society
Starting Page	3207
Ending Page	3216
Page Count	10
File Size	283575
File Format	PDF
ISSN	00189448
Volume Number	56
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Network coding Error correction Codes Computer errors Power generation economics Reduced instruction set computing Laboratories Information theory Conferences Wireless networks subspace metric Constant-dimension codes constant-weight codes error control codes injection metric network coding random linear network coding rank metric codes subspace codes
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Packing and Covering Properties of Subspace Codes for Error Control in Random Linear Network Coding

A Rank-Metric Approach to Error Control in Random Network Coding

A Matroid Framework for Noncoherent Random Network Communications

Error-Correcting Codes in Projective Spaces Via Rank-Metric Codes and Ferrers Diagrams

Rank Metric Decoder Architectures for Random Linear Network Coding With Error Control

Construction of error-correcting codes for random network coding

Coding for Errors and Erasures in Random Network Coding

Recursive Code Construction for Random Networks

Relative Generalized Rank Weight of Linear Codes and Its Applications to Network Coding

Constant-Rank Codes and Their Connection to Constant-Dimension Codes

Similar Documents

Packing and Covering Properties of Subspace Codes for Error Control in Random Linear Network Coding

A Rank-Metric Approach to Error Control in Random Network Coding

A Matroid Framework for Noncoherent Random Network Communications

Error-Correcting Codes in Projective Spaces Via Rank-Metric Codes and Ferrers Diagrams

Rank Metric Decoder Architectures for Random Linear Network Coding With Error Control

Construction of error-correcting codes for random network coding

Coding for Errors and Erasures in Random Network Coding

Recursive Code Construction for Random Networks

Relative Generalized Rank Weight of Linear Codes and Its Applications to Network Coding

Constant-Rank Codes and Their Connection to Constant-Dimension Codes