{"paper":{"title":"Quantum $(r,\\delta)$-Locally Recoverable BCH and Homothetic-BCH Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","quant-ph"],"primary_cat":"cs.IT","authors_text":"Carlos Galindo, Fernando Hernando, Ryutaroh Matsumoto","submitted_at":"2026-01-30T05:08:59Z","abstract_excerpt":"Quantum $(r,\\delta)$-locally recoverable codes ($(r,\\delta)$-LRCs) are the quantum version of classical $(r,\\delta)$-LRCs designed to recover multiple failures in large-scale distributed and cloud storage systems. A quantum $(r,\\delta)$-LRC, $Q(C)$, can be constructed from an $(r,\\delta)$-LRC, $C$, which is Euclidean or Hermitian dual-containing.\n  This article is devoted to studying how to get quantum $(r,\\delta)$-LRCs from BCH and homothetic-BCH codes. As a consequence, we give pure quantum $(r,\\delta)$-LRCs which are optimal for the Singleton-like bound."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.22567","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.22567/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}