{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WR6ARRCCQNB2UCUTBOXMV3QWF7","short_pith_number":"pith:WR6ARRCC","canonical_record":{"source":{"id":"1102.2350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-11T14:06:19Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"146fef94303e80047a922d93956df7c98eb3af48acd462a49b4de93dc536ab82","abstract_canon_sha256":"e7c6f3f24d8075459bbbbc3b6b967845b7ae1ebfb90cbe64904e58f7eecacd3e"},"schema_version":"1.0"},"canonical_sha256":"b47c08c4428343aa0a930baecaee162fe205343ae91268a2221ebfbe59c270e0","source":{"kind":"arxiv","id":"1102.2350","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2350","created_at":"2026-05-18T04:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2350v1","created_at":"2026-05-18T04:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2350","created_at":"2026-05-18T04:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"WR6ARRCCQNB2","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WR6ARRCCQNB2UCUT","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WR6ARRCC","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WR6ARRCCQNB2UCUTBOXMV3QWF7","target":"record","payload":{"canonical_record":{"source":{"id":"1102.2350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-11T14:06:19Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"146fef94303e80047a922d93956df7c98eb3af48acd462a49b4de93dc536ab82","abstract_canon_sha256":"e7c6f3f24d8075459bbbbc3b6b967845b7ae1ebfb90cbe64904e58f7eecacd3e"},"schema_version":"1.0"},"canonical_sha256":"b47c08c4428343aa0a930baecaee162fe205343ae91268a2221ebfbe59c270e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:56.165849Z","signature_b64":"/e41bc0cswJzZfqCaF4cp9jVdk37PJvcviQ/VK09fbxJM0CpJlzdDdZTO2XTqI1u89b3Re8qhBA+oFk+/DXmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b47c08c4428343aa0a930baecaee162fe205343ae91268a2221ebfbe59c270e0","last_reissued_at":"2026-05-18T04:28:56.165161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:56.165161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.2350","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:28:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGo22Z6od3FO1tRF+0gDcmzADiFLOW6fqLDkESftcIPOswQbAsaeCRd1NiGGEd9RRk6k/UuOqNpNbClHZiX+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:04:41.946081Z"},"content_sha256":"138ca1edf05aeb8adc109f2cbe04869ce413381cdb81c0f6595271836f78383f","schema_version":"1.0","event_id":"sha256:138ca1edf05aeb8adc109f2cbe04869ce413381cdb81c0f6595271836f78383f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WR6ARRCCQNB2UCUTBOXMV3QWF7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The best possible upper bound on the probability of undetected error for linear codes of full support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jinquan Luo, Torleiv Kl{\\o}ve","submitted_at":"2011-02-11T14:06:19Z","abstract_excerpt":"There is a known best possible upper bound on the probability of undetected error for linear codes. The $[n,k;q]$ codes with probability of undetected error meeting the bound have support of size $k$ only. In this note, linear codes of full support ($=n$) are studied. A best possible upper bound on the probability of undetected error for such codes is given, and the codes with probability of undetected error meeting this bound are characterized."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2350","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:28:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z8oSYCFzgUkwaGRRSZ4eyJkKyeNGNF1LtH8Bzg8ZrS3wTeS/R4S/JPNFkSCMJQsYbsyV+8j11EMglnFZQwxuAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:04:41.946775Z"},"content_sha256":"ea32cc59ee2e52dbcaa61d5cd44f45aa21e7c6f6064353d7fb39fbf7f077fa12","schema_version":"1.0","event_id":"sha256:ea32cc59ee2e52dbcaa61d5cd44f45aa21e7c6f6064353d7fb39fbf7f077fa12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WR6ARRCCQNB2UCUTBOXMV3QWF7/bundle.json","state_url":"https://pith.science/pith/WR6ARRCCQNB2UCUTBOXMV3QWF7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WR6ARRCCQNB2UCUTBOXMV3QWF7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T05:04:41Z","links":{"resolver":"https://pith.science/pith/WR6ARRCCQNB2UCUTBOXMV3QWF7","bundle":"https://pith.science/pith/WR6ARRCCQNB2UCUTBOXMV3QWF7/bundle.json","state":"https://pith.science/pith/WR6ARRCCQNB2UCUTBOXMV3QWF7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WR6ARRCCQNB2UCUTBOXMV3QWF7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WR6ARRCCQNB2UCUTBOXMV3QWF7","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":"e7c6f3f24d8075459bbbbc3b6b967845b7ae1ebfb90cbe64904e58f7eecacd3e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-11T14:06:19Z","title_canon_sha256":"146fef94303e80047a922d93956df7c98eb3af48acd462a49b4de93dc536ab82"},"schema_version":"1.0","source":{"id":"1102.2350","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2350","created_at":"2026-05-18T04:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2350v1","created_at":"2026-05-18T04:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2350","created_at":"2026-05-18T04:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"WR6ARRCCQNB2","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WR6ARRCCQNB2UCUT","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WR6ARRCC","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:ea32cc59ee2e52dbcaa61d5cd44f45aa21e7c6f6064353d7fb39fbf7f077fa12","target":"graph","created_at":"2026-05-18T04:28:56Z","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":"There is a known best possible upper bound on the probability of undetected error for linear codes. The $[n,k;q]$ codes with probability of undetected error meeting the bound have support of size $k$ only. In this note, linear codes of full support ($=n$) are studied. A best possible upper bound on the probability of undetected error for such codes is given, and the codes with probability of undetected error meeting this bound are characterized.","authors_text":"Jinquan Luo, Torleiv Kl{\\o}ve","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-11T14:06:19Z","title":"The best possible upper bound on the probability of undetected error for linear codes of full support"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2350","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":"sha256:138ca1edf05aeb8adc109f2cbe04869ce413381cdb81c0f6595271836f78383f","target":"record","created_at":"2026-05-18T04:28:56Z","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":"e7c6f3f24d8075459bbbbc3b6b967845b7ae1ebfb90cbe64904e58f7eecacd3e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-11T14:06:19Z","title_canon_sha256":"146fef94303e80047a922d93956df7c98eb3af48acd462a49b4de93dc536ab82"},"schema_version":"1.0","source":{"id":"1102.2350","kind":"arxiv","version":1}},"canonical_sha256":"b47c08c4428343aa0a930baecaee162fe205343ae91268a2221ebfbe59c270e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b47c08c4428343aa0a930baecaee162fe205343ae91268a2221ebfbe59c270e0","first_computed_at":"2026-05-18T04:28:56.165161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:56.165161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/e41bc0cswJzZfqCaF4cp9jVdk37PJvcviQ/VK09fbxJM0CpJlzdDdZTO2XTqI1u89b3Re8qhBA+oFk+/DXmDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:56.165849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.2350","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:138ca1edf05aeb8adc109f2cbe04869ce413381cdb81c0f6595271836f78383f","sha256:ea32cc59ee2e52dbcaa61d5cd44f45aa21e7c6f6064353d7fb39fbf7f077fa12"],"state_sha256":"1d75533bc9b9608f24d5c561c50582c7d3c953e42049fabfb572ad381add4da1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IL7eYEQCUcHTTgNfwbEvT/+qF8RsaMnu2sKnFR8fKd9gK92cyGMKUo7zIHxpfUKUYNtWUGaIn1+KqdVH5g2GAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:04:41.949415Z","bundle_sha256":"c4c6728c5e204d8fa37a525f0a6b1785c14cc3aa07ed9195bf11d5966e6169ba"}}