{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7XJP75AXC64GGMWOUZJZ7AAUWE","short_pith_number":"pith:7XJP75AX","schema_version":"1.0","canonical_sha256":"fdd2fff41717b86332cea6539f8014b128d089ac7b79d59783f3ac6a4ed9361b","source":{"kind":"arxiv","id":"1806.05929","version":1},"attestation_state":"computed","paper":{"title":"Rank-metric codes, linear sets, and their duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geertrui Van de Voorde, John Sheekey","submitted_at":"2018-06-15T12:29:01Z","abstract_excerpt":"In this paper we investigate connections between linear sets and subspaces of linear maps. We give a geometric interpretation of the results of [18, Section 5] on linear sets on a projective line. We extend this to linear sets in arbitrary dimension, giving the connection between two constructions for linear sets defined in [9]. Finally, we then exploit this connection by using the MacWilliams identities to obtain information about the possible weight distribution of a linear set of rank n on a projective line $PG(1, q^n)$."},"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":"1806.05929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-15T12:29:01Z","cross_cats_sorted":[],"title_canon_sha256":"00f8e8479f17a977b05a1a84cc6eeedafc2f58bea87c0a805bae5d9be24b792a","abstract_canon_sha256":"7a828b184f0c2a226e88d45f69536530da5f84ec5b09255e8bbfa404cad1582c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:08.995186Z","signature_b64":"1uAThcPJJ+YMnGj0fCEDYCsEmMJ3EzKS5srnbtqgFJmMZSrsH9L0i56Mvsgs+GqoKzabOQIJDfFVQQZhsagpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdd2fff41717b86332cea6539f8014b128d089ac7b79d59783f3ac6a4ed9361b","last_reissued_at":"2026-05-18T00:13:08.994300Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:08.994300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rank-metric codes, linear sets, and their duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geertrui Van de Voorde, John Sheekey","submitted_at":"2018-06-15T12:29:01Z","abstract_excerpt":"In this paper we investigate connections between linear sets and subspaces of linear maps. We give a geometric interpretation of the results of [18, Section 5] on linear sets on a projective line. We extend this to linear sets in arbitrary dimension, giving the connection between two constructions for linear sets defined in [9]. Finally, we then exploit this connection by using the MacWilliams identities to obtain information about the possible weight distribution of a linear set of rank n on a projective line $PG(1, q^n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05929","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":"1806.05929","created_at":"2026-05-18T00:13:08.994471+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.05929v1","created_at":"2026-05-18T00:13:08.994471+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05929","created_at":"2026-05-18T00:13:08.994471+00:00"},{"alias_kind":"pith_short_12","alias_value":"7XJP75AXC64G","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7XJP75AXC64GGMWO","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7XJP75AX","created_at":"2026-05-18T12:32:11.075285+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/7XJP75AXC64GGMWOUZJZ7AAUWE","json":"https://pith.science/pith/7XJP75AXC64GGMWOUZJZ7AAUWE.json","graph_json":"https://pith.science/api/pith-number/7XJP75AXC64GGMWOUZJZ7AAUWE/graph.json","events_json":"https://pith.science/api/pith-number/7XJP75AXC64GGMWOUZJZ7AAUWE/events.json","paper":"https://pith.science/paper/7XJP75AX"},"agent_actions":{"view_html":"https://pith.science/pith/7XJP75AXC64GGMWOUZJZ7AAUWE","download_json":"https://pith.science/pith/7XJP75AXC64GGMWOUZJZ7AAUWE.json","view_paper":"https://pith.science/paper/7XJP75AX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.05929&json=true","fetch_graph":"https://pith.science/api/pith-number/7XJP75AXC64GGMWOUZJZ7AAUWE/graph.json","fetch_events":"https://pith.science/api/pith-number/7XJP75AXC64GGMWOUZJZ7AAUWE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7XJP75AXC64GGMWOUZJZ7AAUWE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7XJP75AXC64GGMWOUZJZ7AAUWE/action/storage_attestation","attest_author":"https://pith.science/pith/7XJP75AXC64GGMWOUZJZ7AAUWE/action/author_attestation","sign_citation":"https://pith.science/pith/7XJP75AXC64GGMWOUZJZ7AAUWE/action/citation_signature","submit_replication":"https://pith.science/pith/7XJP75AXC64GGMWOUZJZ7AAUWE/action/replication_record"}},"created_at":"2026-05-18T00:13:08.994471+00:00","updated_at":"2026-05-18T00:13:08.994471+00:00"}