{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:FO7WU5QRFH6G4GCYJCWXI22IM3","short_pith_number":"pith:FO7WU5QR","schema_version":"1.0","canonical_sha256":"2bbf6a761129fc6e185848ad746b4866ccf4bfac0812708426298e71bf5acd4c","source":{"kind":"arxiv","id":"1409.7408","version":1},"attestation_state":"computed","paper":{"title":"LP-decodable multipermutation codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Stark C. Draper, Xishuo Liu","submitted_at":"2014-09-25T20:09:01Z","abstract_excerpt":"In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that may consist of duplicate entries. We first introduce a new class of matrices called multipermutation matrices. We characterize the convex hull of multipermutation matrices. Based on this characterization, we propose a new class of codes that we term LP-decodable multipermutation codes. Then, we derive two LP decoding algorithms. We first formulate an LP decoding problem for memoryless channels. We then derive an LP algorithm that minimizes the Chebysh"},"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":"1409.7408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-09-25T20:09:01Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"78575eaa60fdec37bac77e518739f6c53b5fce8376ebbf5e5c16e680ad546ba2","abstract_canon_sha256":"eb535dd0d3f8d01dc18399c02ae3ee0c2b8bdbcc1461dee074caad55d725b851"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:52.763873Z","signature_b64":"voV4I0nLICeQ/9v+T+9sAlWkdBkIyoIbdzQ6e8Sh7UA8dyRQEicsKPFC2Llur1MTvyd8ZQn7IqK/lhSH+9QvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2bbf6a761129fc6e185848ad746b4866ccf4bfac0812708426298e71bf5acd4c","last_reissued_at":"2026-05-18T02:41:52.763242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:52.763242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"LP-decodable multipermutation codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Stark C. Draper, Xishuo Liu","submitted_at":"2014-09-25T20:09:01Z","abstract_excerpt":"In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that may consist of duplicate entries. We first introduce a new class of matrices called multipermutation matrices. We characterize the convex hull of multipermutation matrices. Based on this characterization, we propose a new class of codes that we term LP-decodable multipermutation codes. Then, we derive two LP decoding algorithms. We first formulate an LP decoding problem for memoryless channels. We then derive an LP algorithm that minimizes the Chebysh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7408","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":"1409.7408","created_at":"2026-05-18T02:41:52.763349+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.7408v1","created_at":"2026-05-18T02:41:52.763349+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7408","created_at":"2026-05-18T02:41:52.763349+00:00"},{"alias_kind":"pith_short_12","alias_value":"FO7WU5QRFH6G","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"FO7WU5QRFH6G4GCY","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"FO7WU5QR","created_at":"2026-05-18T12:28:28.263976+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/FO7WU5QRFH6G4GCYJCWXI22IM3","json":"https://pith.science/pith/FO7WU5QRFH6G4GCYJCWXI22IM3.json","graph_json":"https://pith.science/api/pith-number/FO7WU5QRFH6G4GCYJCWXI22IM3/graph.json","events_json":"https://pith.science/api/pith-number/FO7WU5QRFH6G4GCYJCWXI22IM3/events.json","paper":"https://pith.science/paper/FO7WU5QR"},"agent_actions":{"view_html":"https://pith.science/pith/FO7WU5QRFH6G4GCYJCWXI22IM3","download_json":"https://pith.science/pith/FO7WU5QRFH6G4GCYJCWXI22IM3.json","view_paper":"https://pith.science/paper/FO7WU5QR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.7408&json=true","fetch_graph":"https://pith.science/api/pith-number/FO7WU5QRFH6G4GCYJCWXI22IM3/graph.json","fetch_events":"https://pith.science/api/pith-number/FO7WU5QRFH6G4GCYJCWXI22IM3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FO7WU5QRFH6G4GCYJCWXI22IM3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FO7WU5QRFH6G4GCYJCWXI22IM3/action/storage_attestation","attest_author":"https://pith.science/pith/FO7WU5QRFH6G4GCYJCWXI22IM3/action/author_attestation","sign_citation":"https://pith.science/pith/FO7WU5QRFH6G4GCYJCWXI22IM3/action/citation_signature","submit_replication":"https://pith.science/pith/FO7WU5QRFH6G4GCYJCWXI22IM3/action/replication_record"}},"created_at":"2026-05-18T02:41:52.763349+00:00","updated_at":"2026-05-18T02:41:52.763349+00:00"}