  Consider a systematic linear code where some (local) parity symbols depend on
few prescribed symbols, while other (heavy) parity symbols may depend on all
data symbols. Local parities allow to quickly recover any single symbol when it
is erased, while heavy parities provide tolerance to a large number of
simultaneous erasures. A code as above is maximally-recoverable if it corrects
all erasure patterns which are information theoretically recoverable given the
code topology. In this paper we present explicit families of
maximally-recoverable codes with locality. We also initiate the study of the
trade-off between maximal recoverability and alphabet size.
