Quantum $(r,δ)$-locally recoverable codes ($(r,δ)$-LRCs) are the quantum version of classical $(r,δ)$-LRCs designed to recover multiple failures in large-scale distributed and cloud storage systems. A quantum $(r,δ)$-LRC, $Q(C)$, can be constructed from an $(r,δ)$-LRC, $C$, which is Euclidean or Hermitian dual-containing. This article is devoted to studying how to get quantum $(r,δ)$-LRCs from BCH and homothetic-BCH codes. As a consequence, we give pure quantum $(r,δ)$-LRCs which are optimal for the Singleton-like bound.

翻译：量子$(r,\delta)$-局部可恢复码（$(r,\delta)$-LRCs）是经典$(r,\delta)$-LRCs的量子版本，旨在恢复大规模分布式与云存储系统中的多重故障。一个量子$(r,\delta)$-LRC，$Q(C)$，可以从一个欧几里得或厄米特对偶包含的$(r,\delta)$-LRC $C$构造而成。本文致力于研究如何从BCH码与相似BCH码获得量子$(r,\delta)$-LRCs。作为结果，我们给出了纯量子$(r,\delta)$-LRCs，这些码对于类Singleton界是最优的。