On the Minimum Length of Functional Batch Codes with Small Recovery Sets

Batch codes are of potential use for load balancing and private information retrieval in distributed data storage systems. Recently, a special case of batch codes, termed functional batch codes, was proposed in the literature. In functional batch codes, users can query linear combinations of the information symbols, and not only the information symbols themselves, as is the case for standard batch codes. In this work, we consider linear functional batch codes with the additional property that every query is answered by using only a small number of coded symbols. We derive bounds on the minimum length of such codes, and evaluate the results by numerical computations.