  In this work we present a class of locally recoverable codes, i.e. codes
where an erasure at a position $P$ of a codeword may be recovered from the
knowledge of the entries in the positions of a recovery set $R_P$. The codes in
the class that we define have availability, meaning that for each position $P$
there are several distinct recovery sets. Also, the entry at position $P$ may
be recovered even in the presence of erasures in some of the positions of the
recovery sets, and the number of supported erasures may vary among the various
recovery sets.
