Bounds for Cooperative Locality Using Generalized Hamming Weights

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