{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:SACPGU3NTDQWSXUSLOEQG7HJ4T","short_pith_number":"pith:SACPGU3N","canonical_record":{"source":{"id":"1904.03104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-04-05T14:54:33Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cc109bc3108afa4227e6b85dfd11c0dfdeef3d751ee52fcb10ee26c05fcf18b1","abstract_canon_sha256":"61cedb065d117c5802a820c1290b1b7d477b3fbfac49fbb8a29ee4b8807d17d9"},"schema_version":"1.0"},"canonical_sha256":"9004f3536d98e1695e925b89037ce9e4d6ec6731d5e705cc8a010b17a0333769","source":{"kind":"arxiv","id":"1904.03104","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03104","created_at":"2026-05-17T23:49:18Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03104v1","created_at":"2026-05-17T23:49:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03104","created_at":"2026-05-17T23:49:18Z"},{"alias_kind":"pith_short_12","alias_value":"SACPGU3NTDQW","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SACPGU3NTDQWSXUS","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SACPGU3N","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:SACPGU3NTDQWSXUSLOEQG7HJ4T","target":"record","payload":{"canonical_record":{"source":{"id":"1904.03104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-04-05T14:54:33Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cc109bc3108afa4227e6b85dfd11c0dfdeef3d751ee52fcb10ee26c05fcf18b1","abstract_canon_sha256":"61cedb065d117c5802a820c1290b1b7d477b3fbfac49fbb8a29ee4b8807d17d9"},"schema_version":"1.0"},"canonical_sha256":"9004f3536d98e1695e925b89037ce9e4d6ec6731d5e705cc8a010b17a0333769","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:18.572654Z","signature_b64":"I8ZEv2L+ycPvgsibFT1j2/OHryeTCC3djismnl7wUPAmgFjcVd/WJf/iSKeutfOJ40NE8mSc5daM6N31mVtWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9004f3536d98e1695e925b89037ce9e4d6ec6731d5e705cc8a010b17a0333769","last_reissued_at":"2026-05-17T23:49:18.572113Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:18.572113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.03104","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":"2026-05-17T23:49:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X4HrXrfrolj6nDxMum9uPvC3jkbMTd5G8QyN0mjNJynGFTZfidF34Td/osM7MCz1Z8J+kynWxx1su0b4zq9YAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:18:27.810774Z"},"content_sha256":"a616702891147de6da2d035040c951ed20f78d1534776b87d1cd7b623b631406","schema_version":"1.0","event_id":"sha256:a616702891147de6da2d035040c951ed20f78d1534776b87d1cd7b623b631406"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:SACPGU3NTDQWSXUSLOEQG7HJ4T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\mathbb{F}_{q^n}$-linear rank distance codes and their distinguishers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ferdinando Zullo, Luca Giuzzi","submitted_at":"2019-04-05T14:54:33Z","abstract_excerpt":"For any admissible value of the parameters there exist Maximum Rank distance (shortly MRD) $\\mathbb{F}_{q^n}$-linear codes of $\\mathbb{F}_q^{n\\times n}$. It has been shown in \\cite{H-TNRR} (see also \\cite{ByrneRavagnani}) that, if field extensions large enough are considered, then \\emph{almost all} (rectangular) rank distance codes are MRD. On the other hand, very few families of $\\mathbb{F}_{q^n}$-linear codes are currently known up to equivalence. One of the possible applications of MRD-codes is for McEliece--like public key cryptosystems, as proposed by Gabidulin, Paramonov and Tretjakov in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03104","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":"2026-05-17T23:49:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uC0jheJRl7nin39UOlhpIBppP3hup6rhPmejy4Spmb4XtjZkrIRVrXbdfcnoVa7nyxVTZOvI8Szoh++HCaqjAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:18:27.811373Z"},"content_sha256":"978bd0fd58588aab0f27bc2efcbcac6aeaee78e2c2a3723573a4d2d9ba2062bf","schema_version":"1.0","event_id":"sha256:978bd0fd58588aab0f27bc2efcbcac6aeaee78e2c2a3723573a4d2d9ba2062bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SACPGU3NTDQWSXUSLOEQG7HJ4T/bundle.json","state_url":"https://pith.science/pith/SACPGU3NTDQWSXUSLOEQG7HJ4T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SACPGU3NTDQWSXUSLOEQG7HJ4T/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":"2026-05-26T06:18:27Z","links":{"resolver":"https://pith.science/pith/SACPGU3NTDQWSXUSLOEQG7HJ4T","bundle":"https://pith.science/pith/SACPGU3NTDQWSXUSLOEQG7HJ4T/bundle.json","state":"https://pith.science/pith/SACPGU3NTDQWSXUSLOEQG7HJ4T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SACPGU3NTDQWSXUSLOEQG7HJ4T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SACPGU3NTDQWSXUSLOEQG7HJ4T","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":"61cedb065d117c5802a820c1290b1b7d477b3fbfac49fbb8a29ee4b8807d17d9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-04-05T14:54:33Z","title_canon_sha256":"cc109bc3108afa4227e6b85dfd11c0dfdeef3d751ee52fcb10ee26c05fcf18b1"},"schema_version":"1.0","source":{"id":"1904.03104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03104","created_at":"2026-05-17T23:49:18Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03104v1","created_at":"2026-05-17T23:49:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03104","created_at":"2026-05-17T23:49:18Z"},{"alias_kind":"pith_short_12","alias_value":"SACPGU3NTDQW","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SACPGU3NTDQWSXUS","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SACPGU3N","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:978bd0fd58588aab0f27bc2efcbcac6aeaee78e2c2a3723573a4d2d9ba2062bf","target":"graph","created_at":"2026-05-17T23:49:18Z","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":"For any admissible value of the parameters there exist Maximum Rank distance (shortly MRD) $\\mathbb{F}_{q^n}$-linear codes of $\\mathbb{F}_q^{n\\times n}$. It has been shown in \\cite{H-TNRR} (see also \\cite{ByrneRavagnani}) that, if field extensions large enough are considered, then \\emph{almost all} (rectangular) rank distance codes are MRD. On the other hand, very few families of $\\mathbb{F}_{q^n}$-linear codes are currently known up to equivalence. One of the possible applications of MRD-codes is for McEliece--like public key cryptosystems, as proposed by Gabidulin, Paramonov and Tretjakov in","authors_text":"Ferdinando Zullo, Luca Giuzzi","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-04-05T14:54:33Z","title":"$\\mathbb{F}_{q^n}$-linear rank distance codes and their distinguishers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03104","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:a616702891147de6da2d035040c951ed20f78d1534776b87d1cd7b623b631406","target":"record","created_at":"2026-05-17T23:49:18Z","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":"61cedb065d117c5802a820c1290b1b7d477b3fbfac49fbb8a29ee4b8807d17d9","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-04-05T14:54:33Z","title_canon_sha256":"cc109bc3108afa4227e6b85dfd11c0dfdeef3d751ee52fcb10ee26c05fcf18b1"},"schema_version":"1.0","source":{"id":"1904.03104","kind":"arxiv","version":1}},"canonical_sha256":"9004f3536d98e1695e925b89037ce9e4d6ec6731d5e705cc8a010b17a0333769","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9004f3536d98e1695e925b89037ce9e4d6ec6731d5e705cc8a010b17a0333769","first_computed_at":"2026-05-17T23:49:18.572113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:18.572113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I8ZEv2L+ycPvgsibFT1j2/OHryeTCC3djismnl7wUPAmgFjcVd/WJf/iSKeutfOJ40NE8mSc5daM6N31mVtWAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:18.572654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.03104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a616702891147de6da2d035040c951ed20f78d1534776b87d1cd7b623b631406","sha256:978bd0fd58588aab0f27bc2efcbcac6aeaee78e2c2a3723573a4d2d9ba2062bf"],"state_sha256":"ca313133791cd117cecc90e803741ea241cfd930c1f283ff9b3a9e5bf50ca9a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"625kgiWzlJJrrJNocZQrIoHprbZ0oLlQ3XPRagi5ubHTzYJTFonu3gsP33crbHlobSKH1+VG/zHeDiaCvboXBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T06:18:27.815275Z","bundle_sha256":"e8ec4d8529576141ba75a0993d53180eb96b1e47fc0b44f055072c97efc91361"}}