Random and explicit (r,δ) quantum LRCs and h-level hierarchical QLRCs are constructed via CSS dual-containing codes, with distance bounds, a Singleton-like bound, and an efficient decoder for the Tamo–Barg family.
arXiv preprint arXiv:2601.22567 (2026)
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Three explicit families of quantum (r,δ)-LRCs are built from cyclic codes, two optimal under the quantum Singleton-like bound when pure, with no length bound relative to field size for constructions 2 and 3.
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Quantum Hierarchical Locally Recoverable Codes
Random and explicit (r,δ) quantum LRCs and h-level hierarchical QLRCs are constructed via CSS dual-containing codes, with distance bounds, a Singleton-like bound, and an efficient decoder for the Tamo–Barg family.
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Constructions of Quantum $(r,\delta)$-LRCs from cyclic codes
Three explicit families of quantum (r,δ)-LRCs are built from cyclic codes, two optimal under the quantum Singleton-like bound when pure, with no length bound relative to field size for constructions 2 and 3.