New Results on Erasure Combinatorial Batch Codes

We investigate in this work the problem of Erasure Combinatorial Batch Codes, in which n files are stored on m servers so that every set of n − r servers allows a client to retrieve at most k distinct files by downloading at most t files from each server. Previous studies have solved this problem for the special case of t =1 using Combinatorial Batch Codes. We tackle the general case t ≥ 1 using a generalization of Hall’s theorem. Additionally, we address a realistic scenario in which the retrieved files are consecutive according to some order and provide a simple and optimal solution for this case.