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Existence results and explicit constructions were given for infinitely many values of $r$, $n$, $q$ ($rn$ even) for scattered $\\mathbb{F}_q$-linear sets of rank $rn/2$. In this paper we prove that the bound $rn/2$ is sharp also in the remaining open cases.\n  Recently Sheekey proved that scattered $\\mathbb{F}_q$-linear sets of $\\mathrm{PG}(1,q^n)$ of maximum rank $n$ yield $\\mathbb{F}_q$-linear MRD-codes with dimension $2n$ and minimum distance $n-1","authors_text":"Bence Csajb\\'ok, Ferdinando Zullo, Giuseppe Marino, Olga Polverino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-24T12:13:16Z","title":"Maximum scattered linear sets and MRD-codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06831","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":"sha256:8cd167030c7bb8174e024905a538e00b26d2ab82bcaef32d6ba345da485b61bf","target":"record","created_at":"2026-05-18T00:52:12Z","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":"21f5f67f83a4c9ee7d97876cbaaf873b8a0c08e0652d57586376a59befd6ecc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-24T12:13:16Z","title_canon_sha256":"7ffc87e845f3ef944274c188c139f6794e4819b36ef999377c60510d44c63e4f"},"schema_version":"1.0","source":{"id":"1701.06831","kind":"arxiv","version":1}},"canonical_sha256":"087a83210e6ac2e27f52a9f8392467c2656efabe1291214301fbc6aa70b7eea8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"087a83210e6ac2e27f52a9f8392467c2656efabe1291214301fbc6aa70b7eea8","first_computed_at":"2026-05-18T00:52:12.089417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:12.089417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B5SB6I9gVtwa3R8nkQHVagREIHinPNvTW53YGHybIE4Y/ByxW00lKzECULVIhHXlYBoa1U2wi7id4F06SLaFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:12.089851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06831","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cd167030c7bb8174e024905a538e00b26d2ab82bcaef32d6ba345da485b61bf","sha256:ed2166e07de56f2259a21868a6038faea5e4ae60aa57001cdf92a9911014e1ce"],"state_sha256":"29b13cec4390014253cbe3afafc55f0adb0f0224d7b285d71e1ba0f21da68bf4"}