{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VN27VGXOWK7NQW4SQ45QWCF5DM","short_pith_number":"pith:VN27VGXO","schema_version":"1.0","canonical_sha256":"ab75fa9aeeb2bed85b92873b0b08bd1b25879b2a337efbe8ea39afd36d205b28","source":{"kind":"arxiv","id":"1509.07337","version":1},"attestation_state":"computed","paper":{"title":"A new class of rank-metric codes and their list decoding beyond the unique decoding radius","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chaoping Xing, Chen Yuan","submitted_at":"2015-09-24T12:25:07Z","abstract_excerpt":"Compared with classical block codes, efficient list decoding of rank-metric codes seems more difficult. Although the list decodability of random rank-metric codes and limits to list decodability have been completely determined, little work on efficient list decoding rank-metric codes has been done. The only known efficient list decoding of rank-metric codes $\\mC$ gives decoding radius up to the Singleton bound $1-R-\\Ge$ with positive rate $R$ when $\\rho(\\mC)$ is extremely small, i.e., $\\Theta(\\Ge^2)$ , where $\\rho(\\mC)$ denotes the ratio of the number of rows over the number of columns of $\\mC"},"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":"1509.07337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-24T12:25:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cb9a653ebc0a44457b90ec5278933f0d04c197fc20c10c401dfb2bd51954ce23","abstract_canon_sha256":"e6a749be003df183596145247e966e9ef286ea4463e4d78c695003053adc375d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:09.272150Z","signature_b64":"okCX7Pq9Z5sDaJvozHPgYmlA4WIkVpsSWytXJu+O1GO+C4Q0DOxL41CFQAvHZ8Kbtbbkk8p/+DZnuOJxMKrwBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab75fa9aeeb2bed85b92873b0b08bd1b25879b2a337efbe8ea39afd36d205b28","last_reissued_at":"2026-05-18T01:32:09.271522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:09.271522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new class of rank-metric codes and their list decoding beyond the unique decoding radius","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chaoping Xing, Chen Yuan","submitted_at":"2015-09-24T12:25:07Z","abstract_excerpt":"Compared with classical block codes, efficient list decoding of rank-metric codes seems more difficult. Although the list decodability of random rank-metric codes and limits to list decodability have been completely determined, little work on efficient list decoding rank-metric codes has been done. The only known efficient list decoding of rank-metric codes $\\mC$ gives decoding radius up to the Singleton bound $1-R-\\Ge$ with positive rate $R$ when $\\rho(\\mC)$ is extremely small, i.e., $\\Theta(\\Ge^2)$ , where $\\rho(\\mC)$ denotes the ratio of the number of rows over the number of columns of $\\mC"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07337","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":"1509.07337","created_at":"2026-05-18T01:32:09.271628+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.07337v1","created_at":"2026-05-18T01:32:09.271628+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07337","created_at":"2026-05-18T01:32:09.271628+00:00"},{"alias_kind":"pith_short_12","alias_value":"VN27VGXOWK7N","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"VN27VGXOWK7NQW4S","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"VN27VGXO","created_at":"2026-05-18T12:29:47.479230+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/VN27VGXOWK7NQW4SQ45QWCF5DM","json":"https://pith.science/pith/VN27VGXOWK7NQW4SQ45QWCF5DM.json","graph_json":"https://pith.science/api/pith-number/VN27VGXOWK7NQW4SQ45QWCF5DM/graph.json","events_json":"https://pith.science/api/pith-number/VN27VGXOWK7NQW4SQ45QWCF5DM/events.json","paper":"https://pith.science/paper/VN27VGXO"},"agent_actions":{"view_html":"https://pith.science/pith/VN27VGXOWK7NQW4SQ45QWCF5DM","download_json":"https://pith.science/pith/VN27VGXOWK7NQW4SQ45QWCF5DM.json","view_paper":"https://pith.science/paper/VN27VGXO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.07337&json=true","fetch_graph":"https://pith.science/api/pith-number/VN27VGXOWK7NQW4SQ45QWCF5DM/graph.json","fetch_events":"https://pith.science/api/pith-number/VN27VGXOWK7NQW4SQ45QWCF5DM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VN27VGXOWK7NQW4SQ45QWCF5DM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VN27VGXOWK7NQW4SQ45QWCF5DM/action/storage_attestation","attest_author":"https://pith.science/pith/VN27VGXOWK7NQW4SQ45QWCF5DM/action/author_attestation","sign_citation":"https://pith.science/pith/VN27VGXOWK7NQW4SQ45QWCF5DM/action/citation_signature","submit_replication":"https://pith.science/pith/VN27VGXOWK7NQW4SQ45QWCF5DM/action/replication_record"}},"created_at":"2026-05-18T01:32:09.271628+00:00","updated_at":"2026-05-18T01:32:09.271628+00:00"}