{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:V7JJ2QRHYMAEZBMUKCUTKZNYCP","short_pith_number":"pith:V7JJ2QRH","canonical_record":{"source":{"id":"1305.1091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-05-06T06:12:15Z","cross_cats_sorted":["math.AC","math.AG","math.IT"],"title_canon_sha256":"ba07eef83250e513b3c12bf4868b178ba5becfebaf820b951c7add36326e9337","abstract_canon_sha256":"5d6acc8d6c3642a5dd5963b4078079ff63002acd11d9e77b656044971991cb72"},"schema_version":"1.0"},"canonical_sha256":"afd29d4227c3004c859450a93565b813d38bbfa422d7bf4cb26447bded7c5171","source":{"kind":"arxiv","id":"1305.1091","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1091","created_at":"2026-05-18T03:26:24Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1091v1","created_at":"2026-05-18T03:26:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1091","created_at":"2026-05-18T03:26:24Z"},{"alias_kind":"pith_short_12","alias_value":"V7JJ2QRHYMAE","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V7JJ2QRHYMAEZBMU","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V7JJ2QRH","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:V7JJ2QRHYMAEZBMUKCUTKZNYCP","target":"record","payload":{"canonical_record":{"source":{"id":"1305.1091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-05-06T06:12:15Z","cross_cats_sorted":["math.AC","math.AG","math.IT"],"title_canon_sha256":"ba07eef83250e513b3c12bf4868b178ba5becfebaf820b951c7add36326e9337","abstract_canon_sha256":"5d6acc8d6c3642a5dd5963b4078079ff63002acd11d9e77b656044971991cb72"},"schema_version":"1.0"},"canonical_sha256":"afd29d4227c3004c859450a93565b813d38bbfa422d7bf4cb26447bded7c5171","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:24.165388Z","signature_b64":"TgwfPUV3OVY/UXg7uGXfMmVrhxO6D5MPMrgJYy+XCNC0+gPYAmu/Wz6EKPIoEpJTzCVqYsMBqcIMM9UFNwkJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afd29d4227c3004c859450a93565b813d38bbfa422d7bf4cb26447bded7c5171","last_reissued_at":"2026-05-18T03:26:24.164799Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:24.164799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.1091","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":"2026-05-18T03:26:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHuoLoglRnxNyCQZVwmFfrI0/0LB6mXSqgKvYRfIo1wyV7rVCoqTDwh8yUoRrp3uSYVZj4Ivq59GLWdx+BlkDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:28:53.488536Z"},"content_sha256":"220bf8556aa365d0c7421e357d751d8fe2b73536ff1ed3b48bfcb8d10304a5b6","schema_version":"1.0","event_id":"sha256:220bf8556aa365d0c7421e357d751d8fe2b73536ff1ed3b48bfcb8d10304a5b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:V7JJ2QRHYMAEZBMUKCUTKZNYCP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Further improvements on the Feng-Rao bound for dual codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG","math.IT"],"primary_cat":"cs.IT","authors_text":"Olav Geil, Stefano Martin","submitted_at":"2013-05-06T06:12:15Z","abstract_excerpt":"Salazar, Dunn and Graham in [Salazar et. al., 2006] presented an improved Feng-Rao bound for the minimum distance of dual codes. In this work we take the improvement a step further. Both the original bound by Salazar et. al., as well as our improvement are lifted so that they deal with generalized Hamming weights. We also demonstrate the advantage of working with one-way well-behaving pairs rather than weakly well-behaving or well-behaving pairs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1091","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":"2026-05-18T03:26:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jLlOqaf/CrNfQqOSkg7mzfpmpe3YO4AsCVFBw29OToKnQOR1zU5U93CX7xGtF74InXmo51smrmF7nLuIGAHxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:28:53.488877Z"},"content_sha256":"8ad04c366fd748ccde3ad02ae1043f3e22f14c5a8cf28899b77d5ce0916d9383","schema_version":"1.0","event_id":"sha256:8ad04c366fd748ccde3ad02ae1043f3e22f14c5a8cf28899b77d5ce0916d9383"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7JJ2QRHYMAEZBMUKCUTKZNYCP/bundle.json","state_url":"https://pith.science/pith/V7JJ2QRHYMAEZBMUKCUTKZNYCP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7JJ2QRHYMAEZBMUKCUTKZNYCP/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":"2026-07-02T21:28:53Z","links":{"resolver":"https://pith.science/pith/V7JJ2QRHYMAEZBMUKCUTKZNYCP","bundle":"https://pith.science/pith/V7JJ2QRHYMAEZBMUKCUTKZNYCP/bundle.json","state":"https://pith.science/pith/V7JJ2QRHYMAEZBMUKCUTKZNYCP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7JJ2QRHYMAEZBMUKCUTKZNYCP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V7JJ2QRHYMAEZBMUKCUTKZNYCP","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":"5d6acc8d6c3642a5dd5963b4078079ff63002acd11d9e77b656044971991cb72","cross_cats_sorted":["math.AC","math.AG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-05-06T06:12:15Z","title_canon_sha256":"ba07eef83250e513b3c12bf4868b178ba5becfebaf820b951c7add36326e9337"},"schema_version":"1.0","source":{"id":"1305.1091","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1091","created_at":"2026-05-18T03:26:24Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1091v1","created_at":"2026-05-18T03:26:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1091","created_at":"2026-05-18T03:26:24Z"},{"alias_kind":"pith_short_12","alias_value":"V7JJ2QRHYMAE","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"V7JJ2QRHYMAEZBMU","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"V7JJ2QRH","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:8ad04c366fd748ccde3ad02ae1043f3e22f14c5a8cf28899b77d5ce0916d9383","target":"graph","created_at":"2026-05-18T03:26:24Z","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":"Salazar, Dunn and Graham in [Salazar et. al., 2006] presented an improved Feng-Rao bound for the minimum distance of dual codes. In this work we take the improvement a step further. Both the original bound by Salazar et. al., as well as our improvement are lifted so that they deal with generalized Hamming weights. We also demonstrate the advantage of working with one-way well-behaving pairs rather than weakly well-behaving or well-behaving pairs.","authors_text":"Olav Geil, Stefano Martin","cross_cats":["math.AC","math.AG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-05-06T06:12:15Z","title":"Further improvements on the Feng-Rao bound for dual codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1091","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":"sha256:220bf8556aa365d0c7421e357d751d8fe2b73536ff1ed3b48bfcb8d10304a5b6","target":"record","created_at":"2026-05-18T03:26:24Z","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":"5d6acc8d6c3642a5dd5963b4078079ff63002acd11d9e77b656044971991cb72","cross_cats_sorted":["math.AC","math.AG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-05-06T06:12:15Z","title_canon_sha256":"ba07eef83250e513b3c12bf4868b178ba5becfebaf820b951c7add36326e9337"},"schema_version":"1.0","source":{"id":"1305.1091","kind":"arxiv","version":1}},"canonical_sha256":"afd29d4227c3004c859450a93565b813d38bbfa422d7bf4cb26447bded7c5171","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afd29d4227c3004c859450a93565b813d38bbfa422d7bf4cb26447bded7c5171","first_computed_at":"2026-05-18T03:26:24.164799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:24.164799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TgwfPUV3OVY/UXg7uGXfMmVrhxO6D5MPMrgJYy+XCNC0+gPYAmu/Wz6EKPIoEpJTzCVqYsMBqcIMM9UFNwkJDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:24.165388Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1091","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:220bf8556aa365d0c7421e357d751d8fe2b73536ff1ed3b48bfcb8d10304a5b6","sha256:8ad04c366fd748ccde3ad02ae1043f3e22f14c5a8cf28899b77d5ce0916d9383"],"state_sha256":"80b08651abcec40de9d6f57539806e1292f4b7eea9dfd8f1b8c14003b894d16a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QaMTc9Zg9FOWbPo3d69NC94yA51H/p04+2ZwC7llFBxVp0FaAN7vfxLySWlzxcYqCRXJCYcWvyVKn2/eGEnLCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T21:28:53.491868Z","bundle_sha256":"ce59b20c09209c621b0160f5fb053a2402fb2b1eb5ba3f1523f2776591a219c1"}}