{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:TZB3E3GLECJPODAE2MDJWQCNGS","short_pith_number":"pith:TZB3E3GL","schema_version":"1.0","canonical_sha256":"9e43b26ccb2092f70c04d3069b404d34bd1f4910f7608b3024d2f76b9031aee0","source":{"kind":"arxiv","id":"1202.0928","version":3},"attestation_state":"computed","paper":{"title":"Improved quantum hypergraph-product LDPC codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexey A. Kovalev, Leonid P. Pryadko","submitted_at":"2012-02-05T00:26:00Z","abstract_excerpt":"We suggest several techniques to improve the toric codes and the finite-rate generalized toric codes (quantum hypergraph-product codes) recently introduced by Tillich and Z\\'emor. For the usual toric codes, we introduce the rotated lattices specified by two integer-valued periodicity vectors. These codes include the checkerboard codes, and the family of minimal single-qubit-encoding toric codes with block length $n=t^2+(t+1)^2$ and distance $d=2t+1$, $t=1,2,...$. We also suggest several related algebraic constructions which nearly quadruple the rate of the existing hypergraph-product codes."},"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":"1202.0928","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-02-05T00:26:00Z","cross_cats_sorted":[],"title_canon_sha256":"542ed06182f3dc33270a60f84760fd82b69db2ed23c35ee1f8d35f8125aa0daf","abstract_canon_sha256":"6a49922dc0e22db37c64ffeb3650fc03082b53022f35104654ad21a15d99b315"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:05.330043Z","signature_b64":"C3tqFVayzR+JRpOQQr0iJfUOu777VV8PfBO5iZoBvS8Kl52sONHPDREi5gDEVKeXnJO9QOs56XowxcP1llDwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e43b26ccb2092f70c04d3069b404d34bd1f4910f7608b3024d2f76b9031aee0","last_reissued_at":"2026-05-18T03:46:05.329552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:05.329552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved quantum hypergraph-product LDPC codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexey A. Kovalev, Leonid P. Pryadko","submitted_at":"2012-02-05T00:26:00Z","abstract_excerpt":"We suggest several techniques to improve the toric codes and the finite-rate generalized toric codes (quantum hypergraph-product codes) recently introduced by Tillich and Z\\'emor. For the usual toric codes, we introduce the rotated lattices specified by two integer-valued periodicity vectors. These codes include the checkerboard codes, and the family of minimal single-qubit-encoding toric codes with block length $n=t^2+(t+1)^2$ and distance $d=2t+1$, $t=1,2,...$. We also suggest several related algebraic constructions which nearly quadruple the rate of the existing hypergraph-product codes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0928","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1202.0928","created_at":"2026-05-18T03:46:05.329634+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.0928v3","created_at":"2026-05-18T03:46:05.329634+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0928","created_at":"2026-05-18T03:46:05.329634+00:00"},{"alias_kind":"pith_short_12","alias_value":"TZB3E3GLECJP","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"TZB3E3GLECJPODAE","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"TZB3E3GL","created_at":"2026-05-18T12:27:23.164592+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.19062","citing_title":"Fair Decoder Baselines and Rigorous Finite-Size Scaling for Bivariate Bicycle Codes on the Quantum Erasure Channel","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TZB3E3GLECJPODAE2MDJWQCNGS","json":"https://pith.science/pith/TZB3E3GLECJPODAE2MDJWQCNGS.json","graph_json":"https://pith.science/api/pith-number/TZB3E3GLECJPODAE2MDJWQCNGS/graph.json","events_json":"https://pith.science/api/pith-number/TZB3E3GLECJPODAE2MDJWQCNGS/events.json","paper":"https://pith.science/paper/TZB3E3GL"},"agent_actions":{"view_html":"https://pith.science/pith/TZB3E3GLECJPODAE2MDJWQCNGS","download_json":"https://pith.science/pith/TZB3E3GLECJPODAE2MDJWQCNGS.json","view_paper":"https://pith.science/paper/TZB3E3GL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.0928&json=true","fetch_graph":"https://pith.science/api/pith-number/TZB3E3GLECJPODAE2MDJWQCNGS/graph.json","fetch_events":"https://pith.science/api/pith-number/TZB3E3GLECJPODAE2MDJWQCNGS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TZB3E3GLECJPODAE2MDJWQCNGS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TZB3E3GLECJPODAE2MDJWQCNGS/action/storage_attestation","attest_author":"https://pith.science/pith/TZB3E3GLECJPODAE2MDJWQCNGS/action/author_attestation","sign_citation":"https://pith.science/pith/TZB3E3GLECJPODAE2MDJWQCNGS/action/citation_signature","submit_replication":"https://pith.science/pith/TZB3E3GLECJPODAE2MDJWQCNGS/action/replication_record"}},"created_at":"2026-05-18T03:46:05.329634+00:00","updated_at":"2026-05-18T03:46:05.329634+00:00"}