{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PK4HGQAQZCM5EJ3SJRNPS42VVP","short_pith_number":"pith:PK4HGQAQ","schema_version":"1.0","canonical_sha256":"7ab8734010c899d227724c5af97355abc72ee96f46dc0d8c7f6122ffd9c5c9cc","source":{"kind":"arxiv","id":"1506.02865","version":1},"attestation_state":"computed","paper":{"title":"On defining generalized rank weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Relinde Jurrius, Ruud Pellikaan","submitted_at":"2015-06-09T11:50:50Z","abstract_excerpt":"This paper investigates the generalized rank weights, with a definition implied by the study of the generalized rank weight enumerator. We study rank metric codes over $L$, where $L$ is a finite Galois extension of a field $K$. This is a generalization of the case where $K = \\mathbb{F}_q$ and $L = \\mathbb{F}_{q^m}$ of Gabidulin codes to arbitrary characteristic. We show equivalence to previous definitions, in particular the ones by Kurihara-Matsumoto-Uyematsu, Oggier-Sboui and Ducoat. As an application of the notion of generalized rank weights, we discuss codes that are degenerate with respect"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.02865","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-09T11:50:50Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"7c7effd1ba0286740283862419a1e89dfb6c5022807b23e4532004902f7d4a7f","abstract_canon_sha256":"2667efbfda3452436c75f9d58d9f7645ce976ced3e7170e49227b855f8fc5b23"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:21.707122Z","signature_b64":"1G0JgsCya5ecT3YbBl8LXgrREdMr6AbpGJpU4Mda5T8HuU/LX5IjvbTUSCJFKVpl1qScWw0dDeTVZtpk2KScBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ab8734010c899d227724c5af97355abc72ee96f46dc0d8c7f6122ffd9c5c9cc","last_reissued_at":"2026-05-18T00:32:21.706416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:21.706416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On defining generalized rank weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Relinde Jurrius, Ruud Pellikaan","submitted_at":"2015-06-09T11:50:50Z","abstract_excerpt":"This paper investigates the generalized rank weights, with a definition implied by the study of the generalized rank weight enumerator. We study rank metric codes over $L$, where $L$ is a finite Galois extension of a field $K$. This is a generalization of the case where $K = \\mathbb{F}_q$ and $L = \\mathbb{F}_{q^m}$ of Gabidulin codes to arbitrary characteristic. We show equivalence to previous definitions, in particular the ones by Kurihara-Matsumoto-Uyematsu, Oggier-Sboui and Ducoat. As an application of the notion of generalized rank weights, we discuss codes that are degenerate with respect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02865","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.02865","created_at":"2026-05-18T00:32:21.706532+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.02865v1","created_at":"2026-05-18T00:32:21.706532+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02865","created_at":"2026-05-18T00:32:21.706532+00:00"},{"alias_kind":"pith_short_12","alias_value":"PK4HGQAQZCM5","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PK4HGQAQZCM5EJ3S","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PK4HGQAQ","created_at":"2026-05-18T12:29:37.295048+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PK4HGQAQZCM5EJ3SJRNPS42VVP","json":"https://pith.science/pith/PK4HGQAQZCM5EJ3SJRNPS42VVP.json","graph_json":"https://pith.science/api/pith-number/PK4HGQAQZCM5EJ3SJRNPS42VVP/graph.json","events_json":"https://pith.science/api/pith-number/PK4HGQAQZCM5EJ3SJRNPS42VVP/events.json","paper":"https://pith.science/paper/PK4HGQAQ"},"agent_actions":{"view_html":"https://pith.science/pith/PK4HGQAQZCM5EJ3SJRNPS42VVP","download_json":"https://pith.science/pith/PK4HGQAQZCM5EJ3SJRNPS42VVP.json","view_paper":"https://pith.science/paper/PK4HGQAQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.02865&json=true","fetch_graph":"https://pith.science/api/pith-number/PK4HGQAQZCM5EJ3SJRNPS42VVP/graph.json","fetch_events":"https://pith.science/api/pith-number/PK4HGQAQZCM5EJ3SJRNPS42VVP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PK4HGQAQZCM5EJ3SJRNPS42VVP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PK4HGQAQZCM5EJ3SJRNPS42VVP/action/storage_attestation","attest_author":"https://pith.science/pith/PK4HGQAQZCM5EJ3SJRNPS42VVP/action/author_attestation","sign_citation":"https://pith.science/pith/PK4HGQAQZCM5EJ3SJRNPS42VVP/action/citation_signature","submit_replication":"https://pith.science/pith/PK4HGQAQZCM5EJ3SJRNPS42VVP/action/replication_record"}},"created_at":"2026-05-18T00:32:21.706532+00:00","updated_at":"2026-05-18T00:32:21.706532+00:00"}