{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:S63BF5CJM5XWDCXCT7S66XDW2Z","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":"96ee23921b7ea1dfe870b7b78fc6be95fb64826608a6c797b56c72a5169e02ac","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-01T10:57:05Z","title_canon_sha256":"690860bdf9327e6717a882ae5c9c19623fc78af93a27c8581b13b08765f120f7"},"schema_version":"1.0","source":{"id":"1006.0109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.0109","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"arxiv_version","alias_value":"1006.0109v1","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0109","created_at":"2026-05-18T00:57:57Z"},{"alias_kind":"pith_short_12","alias_value":"S63BF5CJM5XW","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"S63BF5CJM5XWDCXC","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"S63BF5CJ","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:49f2e341b8bbf941d72f823c00d2464429718b2f4771a639833679760491e512","target":"graph","created_at":"2026-05-18T00:57:57Z","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":"All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact bounds for binary linear codes. Primarily two algorithms considering the dual codes are used, namely extension of dual codes with a proper coordinate, and a fast algorithm for finding a maximum clique in a graph, which is modified to find a maximum set of vectors with the right dependency structure.","authors_text":"Erik Jakobsson, Iliya Bouyukliev","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-01T10:57:05Z","title":"Results on Binary Linear Codes With Minimum Distance 8 and 10"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0109","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":"sha256:1532304ecd421dbd87c6c06ae9a3c1cc997802ec0701b1e51199354a776816c4","target":"record","created_at":"2026-05-18T00:57:57Z","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":"96ee23921b7ea1dfe870b7b78fc6be95fb64826608a6c797b56c72a5169e02ac","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-01T10:57:05Z","title_canon_sha256":"690860bdf9327e6717a882ae5c9c19623fc78af93a27c8581b13b08765f120f7"},"schema_version":"1.0","source":{"id":"1006.0109","kind":"arxiv","version":1}},"canonical_sha256":"97b612f449676f618ae29fe5ef5c76d6423eec55eb5d0c8df86794b269f1cc30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97b612f449676f618ae29fe5ef5c76d6423eec55eb5d0c8df86794b269f1cc30","first_computed_at":"2026-05-18T00:57:57.799568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:57.799568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D7QVn5zsZDhA5e8xWRfIbo/XdcjWyiA/wWNPRhDT5YfEbUytk8jVHxRO3+JN2vcadUafhGoX00gPnhp4J662AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:57.800143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.0109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1532304ecd421dbd87c6c06ae9a3c1cc997802ec0701b1e51199354a776816c4","sha256:49f2e341b8bbf941d72f823c00d2464429718b2f4771a639833679760491e512"],"state_sha256":"0aa579f540b3a7f250f5755b6a1f642a45a8ff0dc4bb6d80c5e7d4d780cecac5"}