Optimal bandwidth efficiency codes are called minimum-bandwidth regenerating (MBR) and attain one of the two extremal points of the optimal Storage-Bandwidth Tradeoff curve  .
MBR codes require minimum repair-bandwidth - a replacement node downloads precisely that data which it wants to store, i.e., . MBR codes then optimize the amount of storage under this condition as . (See here for the system model and notation.)
When a replacement node is constrained to store the same data as the corresponding failed node, the code is known as an exact-MBR code.
Results on MBR Codes (in chronological order)
Exact-repair MBR codes:
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