Bounds for Cooperative Locality Using Generalized Hamming Weights

Conference paper (2017)

Authors

KAS Abdel-Ghaffar University of California
J.H. Weber Discrete Mathematics and Optimization - EEMCS
Research Group
Discrete Mathematics and Optimization (EEMCS) (TU Delft)
Copyright: © 2017 Khaled A.S. Abdel-Ghaffar, J.H. Weber
DOI: https://doi.org/10.1109/ISIT.2017.8006618
Generators Maintenance engineering Electronic mail Linear codes Hamming distance Hamming weight
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Published Date

2017-6

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Discrete Mathematics and Optimization

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.

Files

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