We consider the design of regenerating codes for distributed storage systems
that allow for exact and uncoded (table-based) repair by leveraging the
properties of combinatorial structures known as resolvable designs. 

Our constructions from affine geometries and Hadamard designs allow the design
of systems where a failed node can be exactly regenerated by downloading $\beta$
packets each from a subset of the surviving nodes, where $\beta \geq 1$ (prior
work only considered $\beta = 1$). We also present techniques for the iterative
construction of new codes from existing ones. Our proposed approach allows
system resilience to node failures to be tunable over a large range. We answer
an open question posed in prior work by demonstrating codes that are not derived
from Steiner systems.