{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:T6FEBWCIUGP76VWTUYPPMO2GHV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"89c7a57b95cf710c544a913b174c32873f0dcffa4e8e993506bd113ced0d2433","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-15T00:39:43Z","title_canon_sha256":"6d5b24b99ef304eef6a10198b290625a49400d5093a76fee0d9d810d75f23a66"},"schema_version":"1.0","source":{"id":"1012.3201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3201","created_at":"2026-05-18T04:33:17Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3201v1","created_at":"2026-05-18T04:33:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3201","created_at":"2026-05-18T04:33:17Z"},{"alias_kind":"pith_short_12","alias_value":"T6FEBWCIUGP7","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"T6FEBWCIUGP76VWT","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"T6FEBWCI","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:782c5e15b639168bc117f7f549bf6ad080f77a45c32a3a55ac2609cea5b7ac17","target":"graph","created_at":"2026-05-18T04:33:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in circulant form can be decomposed into descendant cyclic and quasi-cyclic codes of various lengths and rates. Some fundamental structural properties of these descendant codes are developed, including the characterizations of the roots of the generator polynomial of a cyclic descendant code. The second part of the paper shows that cyclic and quasi-cyclic descendant LD","authors_text":"Khaled Abdel-Ghaffar, Qin Huang, Qiuju Diao, Shu Lin","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-15T00:39:43Z","title":"Cyclic and Quasi-Cyclic LDPC Codes on Row and Column Constrained Parity-Check Matrices and Their Trapping Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3201","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b3c47d2f27f83ea073b0e3b4bb214ab530a256e905a05f4c3c5c66267ac77b07","target":"record","created_at":"2026-05-18T04:33:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"89c7a57b95cf710c544a913b174c32873f0dcffa4e8e993506bd113ced0d2433","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-12-15T00:39:43Z","title_canon_sha256":"6d5b24b99ef304eef6a10198b290625a49400d5093a76fee0d9d810d75f23a66"},"schema_version":"1.0","source":{"id":"1012.3201","kind":"arxiv","version":1}},"canonical_sha256":"9f8a40d848a19fff56d3a61ef63b463d574b805f2df97d785b18d56c95df24f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f8a40d848a19fff56d3a61ef63b463d574b805f2df97d785b18d56c95df24f0","first_computed_at":"2026-05-18T04:33:17.542414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:17.542414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6m4yHTKIieRF2cUP5k146MfswyUV/aa9+m2IBzj3EODKKQN3CeoGdQZZ4sGt4AGBiXFgsINnayJvWaTprVo5AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:17.543164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3c47d2f27f83ea073b0e3b4bb214ab530a256e905a05f4c3c5c66267ac77b07","sha256:782c5e15b639168bc117f7f549bf6ad080f77a45c32a3a55ac2609cea5b7ac17"],"state_sha256":"263e6140755c4ad64c0b29949acfafe39ff316f8695d46c92ea1647099b09cca"}