{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:V6TQLTD47ZP2KF4CYQPAKW6YK7","short_pith_number":"pith:V6TQLTD4","schema_version":"1.0","canonical_sha256":"afa705cc7cfe5fa51782c41e055bd857ed4ebf1f80f2be6f01309142f559d27d","source":{"kind":"arxiv","id":"1309.0403","version":2},"attestation_state":"computed","paper":{"title":"On the Geometry of Balls in the Grassmannian and List Decoding of Lifted Gabidulin Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.IT"],"primary_cat":"cs.IT","authors_text":"Anna-Lena Trautmann, Joachim Rosenthal, Natalia Silberstein","submitted_at":"2013-09-02T13:35:35Z","abstract_excerpt":"The finite Grassmannian $\\mathcal{G}_{q}(k,n)$ is defined as the set of all $k$-dimensional subspaces of the ambient space $\\mathbb{F}_{q}^{n}$. Subsets of the finite Grassmannian are called constant dimension codes and have recently found an application in random network coding. In this setting codewords from $\\mathcal{G}_{q}(k,n)$ are sent through a network channel and, since errors may occur during transmission, the received words can possible lie in $\\mathcal{G}_{q}(k',n)$, where $k'\\neq k$. In this paper, we study the balls in $\\mathcal{G}_{q}(k,n)$ with center that is not necessarily in "},"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":"1309.0403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-09-02T13:35:35Z","cross_cats_sorted":["math.AG","math.IT"],"title_canon_sha256":"ecd3a7b24570070d4c9e00c5a98959554561715c0ec6a20008534a6472baeb21","abstract_canon_sha256":"469f7db868b279f341edb4c77265c27f9a7ca19afeb7e8e32856a70d50e6feaa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:28.813624Z","signature_b64":"YPT2nVp0fbnZwGMmRNMYs7KcKTSbXyPZvMpXjIhp2b5reHRoy2VdbzwO53ExygtxpB8JTUpbsxn6jQdGIDOKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afa705cc7cfe5fa51782c41e055bd857ed4ebf1f80f2be6f01309142f559d27d","last_reissued_at":"2026-05-18T02:49:28.812920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:28.812920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Geometry of Balls in the Grassmannian and List Decoding of Lifted Gabidulin Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.IT"],"primary_cat":"cs.IT","authors_text":"Anna-Lena Trautmann, Joachim Rosenthal, Natalia Silberstein","submitted_at":"2013-09-02T13:35:35Z","abstract_excerpt":"The finite Grassmannian $\\mathcal{G}_{q}(k,n)$ is defined as the set of all $k$-dimensional subspaces of the ambient space $\\mathbb{F}_{q}^{n}$. Subsets of the finite Grassmannian are called constant dimension codes and have recently found an application in random network coding. In this setting codewords from $\\mathcal{G}_{q}(k,n)$ are sent through a network channel and, since errors may occur during transmission, the received words can possible lie in $\\mathcal{G}_{q}(k',n)$, where $k'\\neq k$. In this paper, we study the balls in $\\mathcal{G}_{q}(k,n)$ with center that is not necessarily in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0403","kind":"arxiv","version":2},"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":"1309.0403","created_at":"2026-05-18T02:49:28.813029+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.0403v2","created_at":"2026-05-18T02:49:28.813029+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0403","created_at":"2026-05-18T02:49:28.813029+00:00"},{"alias_kind":"pith_short_12","alias_value":"V6TQLTD47ZP2","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"V6TQLTD47ZP2KF4C","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"V6TQLTD4","created_at":"2026-05-18T12:28:04.890932+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/V6TQLTD47ZP2KF4CYQPAKW6YK7","json":"https://pith.science/pith/V6TQLTD47ZP2KF4CYQPAKW6YK7.json","graph_json":"https://pith.science/api/pith-number/V6TQLTD47ZP2KF4CYQPAKW6YK7/graph.json","events_json":"https://pith.science/api/pith-number/V6TQLTD47ZP2KF4CYQPAKW6YK7/events.json","paper":"https://pith.science/paper/V6TQLTD4"},"agent_actions":{"view_html":"https://pith.science/pith/V6TQLTD47ZP2KF4CYQPAKW6YK7","download_json":"https://pith.science/pith/V6TQLTD47ZP2KF4CYQPAKW6YK7.json","view_paper":"https://pith.science/paper/V6TQLTD4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.0403&json=true","fetch_graph":"https://pith.science/api/pith-number/V6TQLTD47ZP2KF4CYQPAKW6YK7/graph.json","fetch_events":"https://pith.science/api/pith-number/V6TQLTD47ZP2KF4CYQPAKW6YK7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V6TQLTD47ZP2KF4CYQPAKW6YK7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V6TQLTD47ZP2KF4CYQPAKW6YK7/action/storage_attestation","attest_author":"https://pith.science/pith/V6TQLTD47ZP2KF4CYQPAKW6YK7/action/author_attestation","sign_citation":"https://pith.science/pith/V6TQLTD47ZP2KF4CYQPAKW6YK7/action/citation_signature","submit_replication":"https://pith.science/pith/V6TQLTD47ZP2KF4CYQPAKW6YK7/action/replication_record"}},"created_at":"2026-05-18T02:49:28.813029+00:00","updated_at":"2026-05-18T02:49:28.813029+00:00"}