We consider the design of regenerating codes for distributed storage systems at the minimum bandwidth regeneration (MBR) point. Our codes consist of an outer MDS code followed by an inner fractional repetition (FR) code (introduced in prior work). In these systems a failed node can be repaired by simply downloading packets from surviving nodes. We present constructions that use the Kronecker product to construct new fractional repetition codes from existing codes. We demonstrate that an infinite family of codes can be generated by considering the Kronecker product of two Steiner systems that have the same storage capacity. The resultant code inherits its normalized repair bandwidth from the storage capacity of the original Steiner systems and has the maximum level of failure resilience possible. We also present some properties of the Kronecker product of resolvable designs and the corresponding file sizes.
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