Coded caching is a technique that generalizes conventional caching and promises significant reductions in traffic over caching networks.
However, the basic coded caching scheme requires that
each file hosted in the server be partitioned into a large number (called the subpacketization level) of non-overlapping subfiles. From a practical perspective, this is problematic as it means that prior schemes are only applicable when the size of the files is extremely large. In this work, we propose coded caching schemes based on combinatorial structures called resolvable designs. These structures can be obtained in a natural manner from linear block codes whose generator matrices possess certain rank properties. We demonstrate that several schemes with subpacketization levels that are exponentially smaller than the basic scheme can be obtained.