Bounds for Cooperative Locality Using Generalized Hamming Weights

Bounds for Cooperative Locality Using Generalized Hamming Weights

Abdel-Ghaffar, Khaled A.S. (University of California)
Weber, J.H. (TU Delft Discrete Mathematics and Optimization)

2017-06

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.

Maintenance engineering
Linear codes
Hamming distance
Hamming weight
Generators
Electronic mail

http://resolver.tudelft.nl/uuid:36a09c51-586a-487f-a175-1113d072745c

https://doi.org/10.1109/ISIT.2017.8006618

IEEE, Piscataway, NJ

978-1-5090-4096-4

Proceedings of the 2017 IEEE International Symposium on Information Theory

2017 IEEE International Symposium on Information Theory, 2017-06-25 → 2017-06-30, Aachen, Germany

Institutional Repository

conference paper

© 2017 Khaled A.S. Abdel-Ghaffar, J.H. Weber