  Locally repairable codes (LRCs) have recently been widely used in distributed
storage systems and the LRCs with $(r,\delta)$-locality ($(r,\delta)$-LRCs)
attracted a lot of interest for tolerating multiple erasures. Ge et al.
constructed $(r,\delta)$-LRCs with unbounded code length and optimal minimum
distance when $\delta+1 \leq d \leq 2\delta$ from the parity-check matrix
equipped with the Vandermonde structure, but the block length is limited by the
size of $\mathbb{F}_q$. In this paper, we propose a more general construction
of $(r,\delta)$-LRCs through the parity-check matrix. Furthermore, with the
help of MDS codes, we give three classes of explicit constructions of optimal
$(r,\delta)$-LRCs with block length beyond $q$. It turns out that 1) our
general construction extends the results of Ge et al. and 2) our explicit
constructions yield some optimal $(r,\delta)$-LRCs with new parameters.
