{"paper":{"title":"Pair-Partition Constructions for CPM-Based Quantum LDPC Codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kenta Kasai, Koki Okada","submitted_at":"2026-07-15T17:59:52Z","abstract_excerpt":"We construct binary Calderbank--Shor--Steane (CSS) quantum low-density parity-check (LDPC) codes from circulant permutation matrices (CPMs). The construction is parameterized by column weight J, row weight L, and prime lift size P. A J x J array of pair partitions imposes linear paired-difference equations on the CPM exponents. These equations give CSS orthogonality. The main finite examples reported here are the (J,L)=(4,12)-regular girth-six code [[372,130,16]] with rate 0.349, and the (J,L)=(4,14)-regular girth-six code [[518,228,16]] with rate 0.440. We also record (J,L)=(3,8)-regular girt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14091","kind":"arxiv","version":1},"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/2607.14091/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"}