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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.14091","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-15T17:59:52Z","cross_cats_sorted":[],"title_canon_sha256":"6b84d6e045475882b2c4369f5c40c77e38dbe5f2ec6793bf98608a8974283fc4","abstract_canon_sha256":"53946ebf9a2e0e9a6afd3d84d00b11610176fea052ab40f5f7c997655f043bdc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:23:24.039461Z","signature_b64":"EX0gWWiJvtJ7mbASrLdijAPcEaH5X1je3fjNFWIgM+a6iEA2pBQvemB5q5eaMOhTvb+zRisJqaHelizD2O/uBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5a65dd8139ba3235862116f5e0ec687840126a87a613a05da1e04861bb30bd3","last_reissued_at":"2026-07-16T01:23:24.038548Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:23:24.038548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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