{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZUQCOUCLBVHHFCQVWPUAKBWZFJ","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":"3a5559ada55f223c7dec079f97199cad603772c1d5a52c15a4c9fd2cb8f65cac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-09T16:07:35Z","title_canon_sha256":"e1cf3d16322874cd873a2e615d02bd304c40b079d85c1744af9283ff9f5e4d83"},"schema_version":"1.0","source":{"id":"1908.03513","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03513","created_at":"2026-07-05T02:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03513v2","created_at":"2026-07-05T02:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03513","created_at":"2026-07-05T02:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"ZUQCOUCLBVHH","created_at":"2026-07-05T02:05:05Z"},{"alias_kind":"pith_short_16","alias_value":"ZUQCOUCLBVHHFCQV","created_at":"2026-07-05T02:05:05Z"},{"alias_kind":"pith_short_8","alias_value":"ZUQCOUCL","created_at":"2026-07-05T02:05:05Z"}],"graph_snapshots":[{"event_id":"sha256:40e2683b482db0e3b0f479abe9fb591be1d935c3e813afcfb3201e99e58b68c1","target":"graph","created_at":"2026-07-05T02:05:05Z","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/1908.03513/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Binary linear codes are constructed from graphs, in particular, by the generator matrix $[I_n|A]$ where $A$ is the adjacency matrix of a graph on $n$ vertices. A combinatorial interpretation of the minimum distance of such codes is given. We also present graph theoretic conditions for such linear codes to be Type I and Type II self-dual. Several examples of binary linear codes produced by well-known graph classes are given.","authors_text":"Bahattin Yildiz, Sudipta Mallik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-09T16:07:35Z","title":"Isodual and Self-dual Codes from Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03513","kind":"arxiv","version":2},"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:dbcca34f1f6c73853daa779bd11981a5db661760c7a38d6f89ebb825e7c80f85","target":"record","created_at":"2026-07-05T02:05:05Z","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":"3a5559ada55f223c7dec079f97199cad603772c1d5a52c15a4c9fd2cb8f65cac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-09T16:07:35Z","title_canon_sha256":"e1cf3d16322874cd873a2e615d02bd304c40b079d85c1744af9283ff9f5e4d83"},"schema_version":"1.0","source":{"id":"1908.03513","kind":"arxiv","version":2}},"canonical_sha256":"cd2027504b0d4e728a15b3e80506d92a79f41d87c376dbc4b054ce2132471b2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd2027504b0d4e728a15b3e80506d92a79f41d87c376dbc4b054ce2132471b2d","first_computed_at":"2026-07-05T02:05:05.340569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:05:05.340569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZGV9DtfQUk/szLO61wtZbLRiZ+HmztAdNv+W6pE9WRVHSnV4QqWJEvAuy3/4Br8Ax1tsjEh24lbsB9Yud46FAw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:05:05.340931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03513","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbcca34f1f6c73853daa779bd11981a5db661760c7a38d6f89ebb825e7c80f85","sha256:40e2683b482db0e3b0f479abe9fb591be1d935c3e813afcfb3201e99e58b68c1"],"state_sha256":"716c640242c88b32de3ac8e70e906063763c8937b3dd9bd5e45122fe452b6b06"}