This paper focuses on a linear code C with all symbol locality such that its code symbols set is partitioned to s disjoint components and every code symbol in each component j has t-pairwise disjoint recovery sets of size rj, for j ∈ {1, 2, . . . , s}, where r1, . . . , rs and t are given integers. Code C is a locally recoverable code with multiple (rj)j∈[s]-localities and availability t and is defined by t −MLs −LRC. We present an upper bound on minimum Hamming distance d for s ≥ 2 and explain the result of the new bound using an example.
