A Class of Codes With Availability and Multiple Local-Erasures Correction

In a locally recoverable code (LRC), any code symbol can be recovered by accessing at most r other symbols (called a recovery set). In an LRC with availability, any information symbol has t disjoint recovery sets. In this letter, we consider a new class of codes with availability, where the l
^th
, 1 ≤ l ≤ t disjoint recovery set for any information symbol has locality rl and it is protected by a local code of minimum Hamming distance at least δ
_l
. We derive an upper-bound on the minimum Hamming distance of these codes. A family of systematic codes with information availability is constructed achieving the bound with equality.