{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:C3I4XEEVGQ2SMORWHSGM635EP5","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":"2bcbfb8a499c68d2a1be3cc1bc52c52bb4146adba4dc1e99a46c1aee01e68f0b","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2005-06-12T09:00:09Z","title_canon_sha256":"5e4eba58313b8343b9dfffc62599f01e6fb72ab16d6a7cef002dfee932383f4a"},"schema_version":"1.0","source":{"id":"cs/0506042","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0506042","created_at":"2026-05-18T00:58:26Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0506042v1","created_at":"2026-05-18T00:58:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0506042","created_at":"2026-05-18T00:58:26Z"},{"alias_kind":"pith_short_12","alias_value":"C3I4XEEVGQ2S","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"C3I4XEEVGQ2SMORW","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"C3I4XEEV","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:0c553d166ab73be66845bb03dee5c439cbf0297b07867e22b1c9d37498f464a7","target":"graph","created_at":"2026-05-18T00:58:26Z","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":"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.","authors_text":"Christine Kelley, Deepak Sridhara, Joachim Rosenthal","cross_cats":["math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2005-06-12T09:00:09Z","title":"Tree-Based Construction of LDPC Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0506042","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":"sha256:2a1625b015c829056b7ba19d81b671d3b1be719190649856ba59082530b4e307","target":"record","created_at":"2026-05-18T00:58:26Z","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":"2bcbfb8a499c68d2a1be3cc1bc52c52bb4146adba4dc1e99a46c1aee01e68f0b","cross_cats_sorted":["math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2005-06-12T09:00:09Z","title_canon_sha256":"5e4eba58313b8343b9dfffc62599f01e6fb72ab16d6a7cef002dfee932383f4a"},"schema_version":"1.0","source":{"id":"cs/0506042","kind":"arxiv","version":1}},"canonical_sha256":"16d1cb90953435263a363c8ccf6fa47f70a77074d5ad129592f24d6148952385","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16d1cb90953435263a363c8ccf6fa47f70a77074d5ad129592f24d6148952385","first_computed_at":"2026-05-18T00:58:26.854812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:26.854812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mcfTIyJrAEdkvw2W5s5YXc3HfcRGZ5GJndGT7BLG7dfdbaDK+jZLzf5za2DCpKjEZtfhqthr0xFF6bgfaN7QAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:26.855588Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0506042","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a1625b015c829056b7ba19d81b671d3b1be719190649856ba59082530b4e307","sha256:0c553d166ab73be66845bb03dee5c439cbf0297b07867e22b1c9d37498f464a7"],"state_sha256":"0e881fa8b91f21d1ab2e0d8aaef7a1fc76d51fa57c25aa4f21bd3dc003e195d6"}