{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:IPHZZ5YZWR55PIKF56NPRQLGS7","short_pith_number":"pith:IPHZZ5YZ","canonical_record":{"source":{"id":"1107.1529","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-07-07T21:49:55Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"121cb2243cb05ed4dc6fc8bc30648748a99ace2185fcc977fdb710eb7d1245ec","abstract_canon_sha256":"693291c346bea7e08086f29f576bc7335532156fbe72a04c7814fd98f5e097dc"},"schema_version":"1.0"},"canonical_sha256":"43cf9cf719b47bd7a145ef9af8c16697ddbc6d0110b9c20a182494762b6f396f","source":{"kind":"arxiv","id":"1107.1529","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1529","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1529v2","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1529","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"pith_short_12","alias_value":"IPHZZ5YZWR55","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"IPHZZ5YZWR55PIKF","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"IPHZZ5YZ","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:IPHZZ5YZWR55PIKF56NPRQLGS7","target":"record","payload":{"canonical_record":{"source":{"id":"1107.1529","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-07-07T21:49:55Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"121cb2243cb05ed4dc6fc8bc30648748a99ace2185fcc977fdb710eb7d1245ec","abstract_canon_sha256":"693291c346bea7e08086f29f576bc7335532156fbe72a04c7814fd98f5e097dc"},"schema_version":"1.0"},"canonical_sha256":"43cf9cf719b47bd7a145ef9af8c16697ddbc6d0110b9c20a182494762b6f396f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:17.723933Z","signature_b64":"wZiihwpm5iSfsWX2hEdLcKzW/8ZhpzUgQ4GYXIu4rgtI7CyuTUNcPfMgHn2kopuiJ8msoHIggSG1bTw+pU0YDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43cf9cf719b47bd7a145ef9af8c16697ddbc6d0110b9c20a182494762b6f396f","last_reissued_at":"2026-05-18T03:28:17.723281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:17.723281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.1529","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:28:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XwtjJg7BQo06I1ZRMNeJ9QkBUWzlckQXM+nFIkx+8npJxnfOIy2GJTQv8L+ewFFQC2ilDvl0avIJLRNWcxcMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T22:34:32.657729Z"},"content_sha256":"c8eaaddf83167210f96d0e0e405e666f586747bba19f59d22a2c36a7e044ff04","schema_version":"1.0","event_id":"sha256:c8eaaddf83167210f96d0e0e405e666f586747bba19f59d22a2c36a7e044ff04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:IPHZZ5YZWR55PIKF56NPRQLGS7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decoding of Matrix-Product Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Diego Ruano, Fernando Hernando","submitted_at":"2011-07-07T21:49:55Z","abstract_excerpt":"We propose a decoding algorithm for the $(u\\mid u+v)$-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one can decode beyond the error correction capability of the code."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1529","kind":"arxiv","version":2},"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":"2026-05-18T03:28:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2QPA6bpVteKWs0FWHYgmqdW6MlTm4ddCRuZ7kLUtQViZ659up/HQwvwQdAkeqJcuYIzI6K0diaLQxMHbxK+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T22:34:32.658068Z"},"content_sha256":"e631e8c4214e82932a73a2b05907c5d1f8193e84ad16acd254d4ddf0b2c2d5d3","schema_version":"1.0","event_id":"sha256:e631e8c4214e82932a73a2b05907c5d1f8193e84ad16acd254d4ddf0b2c2d5d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IPHZZ5YZWR55PIKF56NPRQLGS7/bundle.json","state_url":"https://pith.science/pith/IPHZZ5YZWR55PIKF56NPRQLGS7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IPHZZ5YZWR55PIKF56NPRQLGS7/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":"2026-06-26T22:34:32Z","links":{"resolver":"https://pith.science/pith/IPHZZ5YZWR55PIKF56NPRQLGS7","bundle":"https://pith.science/pith/IPHZZ5YZWR55PIKF56NPRQLGS7/bundle.json","state":"https://pith.science/pith/IPHZZ5YZWR55PIKF56NPRQLGS7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IPHZZ5YZWR55PIKF56NPRQLGS7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IPHZZ5YZWR55PIKF56NPRQLGS7","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":"693291c346bea7e08086f29f576bc7335532156fbe72a04c7814fd98f5e097dc","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-07-07T21:49:55Z","title_canon_sha256":"121cb2243cb05ed4dc6fc8bc30648748a99ace2185fcc977fdb710eb7d1245ec"},"schema_version":"1.0","source":{"id":"1107.1529","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1529","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1529v2","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1529","created_at":"2026-05-18T03:28:17Z"},{"alias_kind":"pith_short_12","alias_value":"IPHZZ5YZWR55","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"IPHZZ5YZWR55PIKF","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"IPHZZ5YZ","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:e631e8c4214e82932a73a2b05907c5d1f8193e84ad16acd254d4ddf0b2c2d5d3","target":"graph","created_at":"2026-05-18T03:28:17Z","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":"We propose a decoding algorithm for the $(u\\mid u+v)$-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one can decode beyond the error correction capability of the code.","authors_text":"Diego Ruano, Fernando Hernando","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-07-07T21:49:55Z","title":"Decoding of Matrix-Product Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1529","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:c8eaaddf83167210f96d0e0e405e666f586747bba19f59d22a2c36a7e044ff04","target":"record","created_at":"2026-05-18T03:28:17Z","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":"693291c346bea7e08086f29f576bc7335532156fbe72a04c7814fd98f5e097dc","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-07-07T21:49:55Z","title_canon_sha256":"121cb2243cb05ed4dc6fc8bc30648748a99ace2185fcc977fdb710eb7d1245ec"},"schema_version":"1.0","source":{"id":"1107.1529","kind":"arxiv","version":2}},"canonical_sha256":"43cf9cf719b47bd7a145ef9af8c16697ddbc6d0110b9c20a182494762b6f396f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43cf9cf719b47bd7a145ef9af8c16697ddbc6d0110b9c20a182494762b6f396f","first_computed_at":"2026-05-18T03:28:17.723281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:17.723281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wZiihwpm5iSfsWX2hEdLcKzW/8ZhpzUgQ4GYXIu4rgtI7CyuTUNcPfMgHn2kopuiJ8msoHIggSG1bTw+pU0YDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:17.723933Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1529","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8eaaddf83167210f96d0e0e405e666f586747bba19f59d22a2c36a7e044ff04","sha256:e631e8c4214e82932a73a2b05907c5d1f8193e84ad16acd254d4ddf0b2c2d5d3"],"state_sha256":"576ca7570f480323044b3e0900574b0bc332102259c24f1ff45180ba2dd1df99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDu9kFYoRzVjj7GagsAcwfYtx2VptQl0OgK0HySj0hKpUJS+jvCRbXuOZhH6+Rmduw9NGeZZnqmAhsqVsNtRCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T22:34:32.660451Z","bundle_sha256":"785704146e89cf6acba0e587cbc2ccc1a4a1fa8cd8d1e1a13b1f7a48fe759e53"}}