{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:C3I4XEEVGQ2SMORWHSGM635EP5","short_pith_number":"pith:C3I4XEEV","schema_version":"1.0","canonical_sha256":"16d1cb90953435263a363c8ccf6fa47f70a77074d5ad129592f24d6148952385","source":{"kind":"arxiv","id":"cs/0506042","version":1},"attestation_state":"computed","paper":{"title":"Tree-Based Construction of LDPC Codes","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Christine Kelley, Deepak Sridhara, Joachim Rosenthal","submitted_at":"2005-06-12T09:00:09Z","abstract_excerpt":"We present a construction of LDPC codes that have minimum pseudocodeword weight equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a d-regular tree for a fixed number of layers and employing a connection algorithm based on mutually orthogonal Latin squares to close the tree. Methods are presented for degrees d=p^s and d = p^s+1, for p a prime, -- one of which includes the well-known finite-geometry-based LDPC 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":"cs/0506042","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.IT","submitted_at":"2005-06-12T09:00:09Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"5e4eba58313b8343b9dfffc62599f01e6fb72ab16d6a7cef002dfee932383f4a","abstract_canon_sha256":"2bcbfb8a499c68d2a1be3cc1bc52c52bb4146adba4dc1e99a46c1aee01e68f0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:26.855588Z","signature_b64":"mcfTIyJrAEdkvw2W5s5YXc3HfcRGZ5GJndGT7BLG7dfdbaDK+jZLzf5za2DCpKjEZtfhqthr0xFF6bgfaN7QAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16d1cb90953435263a363c8ccf6fa47f70a77074d5ad129592f24d6148952385","last_reissued_at":"2026-05-18T00:58:26.854812Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:26.854812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tree-Based Construction of LDPC Codes","license":"","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Christine Kelley, Deepak Sridhara, Joachim Rosenthal","submitted_at":"2005-06-12T09:00:09Z","abstract_excerpt":"We present a construction of LDPC codes that have minimum pseudocodeword weight equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a d-regular tree for a fixed number of layers and employing a connection algorithm based on mutually orthogonal Latin squares to close the tree. Methods are presented for degrees d=p^s and d = p^s+1, for p a prime, -- one of which includes the well-known finite-geometry-based LDPC codes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0506042","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":""},"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":"cs/0506042","created_at":"2026-05-18T00:58:26.854941+00:00"},{"alias_kind":"arxiv_version","alias_value":"cs/0506042v1","created_at":"2026-05-18T00:58:26.854941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0506042","created_at":"2026-05-18T00:58:26.854941+00:00"},{"alias_kind":"pith_short_12","alias_value":"C3I4XEEVGQ2S","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"C3I4XEEVGQ2SMORW","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"C3I4XEEV","created_at":"2026-05-18T12:25:53.335082+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C3I4XEEVGQ2SMORWHSGM635EP5","json":"https://pith.science/pith/C3I4XEEVGQ2SMORWHSGM635EP5.json","graph_json":"https://pith.science/api/pith-number/C3I4XEEVGQ2SMORWHSGM635EP5/graph.json","events_json":"https://pith.science/api/pith-number/C3I4XEEVGQ2SMORWHSGM635EP5/events.json","paper":"https://pith.science/paper/C3I4XEEV"},"agent_actions":{"view_html":"https://pith.science/pith/C3I4XEEVGQ2SMORWHSGM635EP5","download_json":"https://pith.science/pith/C3I4XEEVGQ2SMORWHSGM635EP5.json","view_paper":"https://pith.science/paper/C3I4XEEV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cs/0506042&json=true","fetch_graph":"https://pith.science/api/pith-number/C3I4XEEVGQ2SMORWHSGM635EP5/graph.json","fetch_events":"https://pith.science/api/pith-number/C3I4XEEVGQ2SMORWHSGM635EP5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C3I4XEEVGQ2SMORWHSGM635EP5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C3I4XEEVGQ2SMORWHSGM635EP5/action/storage_attestation","attest_author":"https://pith.science/pith/C3I4XEEVGQ2SMORWHSGM635EP5/action/author_attestation","sign_citation":"https://pith.science/pith/C3I4XEEVGQ2SMORWHSGM635EP5/action/citation_signature","submit_replication":"https://pith.science/pith/C3I4XEEVGQ2SMORWHSGM635EP5/action/replication_record"}},"created_at":"2026-05-18T00:58:26.854941+00:00","updated_at":"2026-05-18T00:58:26.854941+00:00"}