{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WHSLOB4OHEWW7GZCTAGLATJQLJ","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":"215738b92cd8e04aa3645b579adfa42ea255bb3becdfe51201c64dcd007946a8","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2024-02-09T22:38:47Z","title_canon_sha256":"ad9c5bfb0ce70f5f66bf73218e02e4648202d2b1a560a1b03cd8dfbbe285fc60"},"schema_version":"1.0","source":{"id":"2402.06814","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.06814","created_at":"2026-07-05T07:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"2402.06814v1","created_at":"2026-07-05T07:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.06814","created_at":"2026-07-05T07:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"WHSLOB4OHEWW","created_at":"2026-07-05T07:43:38Z"},{"alias_kind":"pith_short_16","alias_value":"WHSLOB4OHEWW7GZC","created_at":"2026-07-05T07:43:38Z"},{"alias_kind":"pith_short_8","alias_value":"WHSLOB4O","created_at":"2026-07-05T07:43:38Z"}],"graph_snapshots":[{"event_id":"sha256:6d714e2ce1507d8566582e6b56be60189461e49e3a734811e619956da12d79de","target":"graph","created_at":"2026-07-05T07:43:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2402.06814/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce fair-density parity-check (FDPC) codes targeting high-rate applications. In particular, we start with a base parity-check matrix $H_b$ of dimension $2 \\sqrt{n} \\times n$, where $n$ is the code block length, and the number of ones in each row and column of $H_b$ is equal to $\\sqrt{n}$ and $2$, respectively. We propose a deterministic combinatorial method for picking the base matrix $H_b$, assuming $n=4t^2$ for some integer $t \\geq 2$. We then extend this by obtaining permuted versions of $H_b$ (e.g., via random permutations of its columns) and stacking them on top of each other lea","authors_text":"Hessam Mahdavifar","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2024-02-09T22:38:47Z","title":"High-Rate Fair-Density Parity-Check Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.06814","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":"sha256:5809044a137c5dd62382f95c93e5546ab581984f63815b8f957ef29000e080a0","target":"record","created_at":"2026-07-05T07:43:38Z","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":"215738b92cd8e04aa3645b579adfa42ea255bb3becdfe51201c64dcd007946a8","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2024-02-09T22:38:47Z","title_canon_sha256":"ad9c5bfb0ce70f5f66bf73218e02e4648202d2b1a560a1b03cd8dfbbe285fc60"},"schema_version":"1.0","source":{"id":"2402.06814","kind":"arxiv","version":1}},"canonical_sha256":"b1e4b7078e392d6f9b22980cb04d305a6ed2be09c3fb12ef31b2dfe32c0fc1c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1e4b7078e392d6f9b22980cb04d305a6ed2be09c3fb12ef31b2dfe32c0fc1c0","first_computed_at":"2026-07-05T07:43:38.996202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:43:38.996202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l+TSkCo2vplaKc01ULMm+RFornx+gR0n+UKebSK9R14GQOdtYxGCgt+chfESJFO4U+THoFqeerlUAHKoIkuAAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:43:38.996660Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.06814","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5809044a137c5dd62382f95c93e5546ab581984f63815b8f957ef29000e080a0","sha256:6d714e2ce1507d8566582e6b56be60189461e49e3a734811e619956da12d79de"],"state_sha256":"37d35ef459615584a39ee306ac51204ea8485e8dbccfd8d5b07ac5f92652b27d"}