Bounds for Cooperative Locality Using Generalized Hamming Weights

Khaled A.S. Abdel-Ghaffar; Jos H. Weber

doi:10.1109/ISIT.2017.8006618

Bounds for Cooperative Locality Using Generalized Hamming Weights

Khaled A.S. Abdel-Ghaffar, Jos H. Weber

Discrete Mathematics and Optimization

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

4 Citations (Scopus)

51 Downloads (Pure)

Abstract

The Cadambe-Mazumdar bound gives a necessary condition for a code to have a certain locality in case of a single erasure in terms of length, dimension, and Hamming distance of the code and of certain shortened codes. The bound has been generalized by Rawat, Mazumdar, and Vishwanath to recover multiple erasures in a cooperative repair scenario. In this paper, the generalized Hamming weights of the code and its shortened codes, which include the Hamming distance as one component, are incorporated to obtain bounds on locality to recover a single
erasure or multiple erasures cooperatively. The new bounds give sharper necessary conditions than existing bounds.

Original language	English
Title of host publication	Proceedings of the 2017 IEEE International Symposium on Information Theory
Place of Publication	Piscataway, NJ
Publisher	IEEE
Pages	699-703
Number of pages	5
ISBN (Electronic)	978-1-5090-4096-4
DOIs	https://doi.org/10.1109/ISIT.2017.8006618
Publication status	Published - Jun 2017
Event	2017 IEEE International Symposium on Information Theory - Aachen, Germany Duration: 25 Jun 2017 → 30 Jun 2017 https://isit2017.org/

Conference

Conference	2017 IEEE International Symposium on Information Theory
Abbreviated title	ISIT 2017
Country/Territory	Germany
City	Aachen
Period	25/06/17 → 30/06/17
Internet address	https://isit2017.org/

Keywords

Maintenance engineering
Linear codes
Hamming distance
Hamming weight
Generators
Electronic mail

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10.1109/ISIT.2017.8006618

ISIT2017_finalAccepted author manuscript, 122 KB

Cite this

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abstract = "The Cadambe-Mazumdar bound gives a necessary condition for a code to have a certain locality in case of a single erasure in terms of length, dimension, and Hamming distance of the code and of certain shortened codes. The bound has been generalized by Rawat, Mazumdar, and Vishwanath to recover multiple erasures in a cooperative repair scenario. In this paper, the generalized Hamming weights of the code and its shortened codes, which include the Hamming distance as one component, are incorporated to obtain bounds on locality to recover a singleerasure or multiple erasures cooperatively. The new bounds give sharper necessary conditions than existing bounds.",

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AB - The Cadambe-Mazumdar bound gives a necessary condition for a code to have a certain locality in case of a single erasure in terms of length, dimension, and Hamming distance of the code and of certain shortened codes. The bound has been generalized by Rawat, Mazumdar, and Vishwanath to recover multiple erasures in a cooperative repair scenario. In this paper, the generalized Hamming weights of the code and its shortened codes, which include the Hamming distance as one component, are incorporated to obtain bounds on locality to recover a singleerasure or multiple erasures cooperatively. The new bounds give sharper necessary conditions than existing bounds.

KW - Maintenance engineering

KW - Linear codes

KW - Hamming distance

KW - Hamming weight

KW - Generators

KW - Electronic mail

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M3 - Conference contribution

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BT - Proceedings of the 2017 IEEE International Symposium on Information Theory

PB - IEEE

CY - Piscataway, NJ

T2 - 2017 IEEE International Symposium on Information Theory

Y2 - 25 June 2017 through 30 June 2017

ER -

Bounds for Cooperative Locality Using Generalized Hamming Weights

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