{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4TBXGNY3KLYDQYHIM57ATSUEH2","short_pith_number":"pith:4TBXGNY3","schema_version":"1.0","canonical_sha256":"e4c373371b52f03860e8677e09ca843ebbcbd4bfbf7fc8fb175debf55c823740","source":{"kind":"arxiv","id":"1406.1067","version":1},"attestation_state":"computed","paper":{"title":"Switchings of semifield multiplications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ferruh \\\"Ozbudak, Xiang-dong Hou, Yue Zhou","submitted_at":"2014-06-04T15:04:19Z","abstract_excerpt":"Let $B(X,Y)$ be a polynomial over $\\mathbb{F}_{q^n}$ which defines an $\\mathbb{F}_q$-bilinear form on the vector space $\\mathbb{F}_{q^n}$, and let $\\xi$ be a nonzero element in $\\mathbb{F}_{q^n}$. In this paper, we consider for which $B(X,Y)$, the binary operation $xy+B(x,y)\\xi$ defines a (pre)semifield multiplication on $\\mathbb{F}_{q^n}$. We prove that this question is equivalent to finding $q$-linearized polynomials $L(X)\\in\\mathbb{F}_{q^n}[X]$ such that $Tr_{q^n/q}(L(x)/x)\\neq 0$ for all $x\\in\\mathbb{F}_{q^n}^*$. For $n\\le 4$, we present several families of $L(X)$ and we investigate the de"},"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":"1406.1067","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-04T15:04:19Z","cross_cats_sorted":[],"title_canon_sha256":"ae001ceb338b1d222704768274eaf624010ebe41f6e8f1559c5a20ee9e58dd38","abstract_canon_sha256":"8347f1d6f31450acdd2ae8570d4fe7c3835b4ccba0546b4b1b2833ad301c906b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:11.852491Z","signature_b64":"A7IaJvtretw0xCynZQDs8rahLBazDETiGvdeuHmxI0vTxZEQ7Y62IQW+JDsQ8kE9QkysTYrJmH+sc9+X67LgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4c373371b52f03860e8677e09ca843ebbcbd4bfbf7fc8fb175debf55c823740","last_reissued_at":"2026-05-18T01:44:11.851744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:11.851744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Switchings of semifield multiplications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ferruh \\\"Ozbudak, Xiang-dong Hou, Yue Zhou","submitted_at":"2014-06-04T15:04:19Z","abstract_excerpt":"Let $B(X,Y)$ be a polynomial over $\\mathbb{F}_{q^n}$ which defines an $\\mathbb{F}_q$-bilinear form on the vector space $\\mathbb{F}_{q^n}$, and let $\\xi$ be a nonzero element in $\\mathbb{F}_{q^n}$. In this paper, we consider for which $B(X,Y)$, the binary operation $xy+B(x,y)\\xi$ defines a (pre)semifield multiplication on $\\mathbb{F}_{q^n}$. We prove that this question is equivalent to finding $q$-linearized polynomials $L(X)\\in\\mathbb{F}_{q^n}[X]$ such that $Tr_{q^n/q}(L(x)/x)\\neq 0$ for all $x\\in\\mathbb{F}_{q^n}^*$. For $n\\le 4$, we present several families of $L(X)$ and we investigate the de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1067","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":"1406.1067","created_at":"2026-05-18T01:44:11.851866+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.1067v1","created_at":"2026-05-18T01:44:11.851866+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1067","created_at":"2026-05-18T01:44:11.851866+00:00"},{"alias_kind":"pith_short_12","alias_value":"4TBXGNY3KLYD","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4TBXGNY3KLYDQYHI","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4TBXGNY3","created_at":"2026-05-18T12:28:14.216126+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/4TBXGNY3KLYDQYHIM57ATSUEH2","json":"https://pith.science/pith/4TBXGNY3KLYDQYHIM57ATSUEH2.json","graph_json":"https://pith.science/api/pith-number/4TBXGNY3KLYDQYHIM57ATSUEH2/graph.json","events_json":"https://pith.science/api/pith-number/4TBXGNY3KLYDQYHIM57ATSUEH2/events.json","paper":"https://pith.science/paper/4TBXGNY3"},"agent_actions":{"view_html":"https://pith.science/pith/4TBXGNY3KLYDQYHIM57ATSUEH2","download_json":"https://pith.science/pith/4TBXGNY3KLYDQYHIM57ATSUEH2.json","view_paper":"https://pith.science/paper/4TBXGNY3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.1067&json=true","fetch_graph":"https://pith.science/api/pith-number/4TBXGNY3KLYDQYHIM57ATSUEH2/graph.json","fetch_events":"https://pith.science/api/pith-number/4TBXGNY3KLYDQYHIM57ATSUEH2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4TBXGNY3KLYDQYHIM57ATSUEH2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4TBXGNY3KLYDQYHIM57ATSUEH2/action/storage_attestation","attest_author":"https://pith.science/pith/4TBXGNY3KLYDQYHIM57ATSUEH2/action/author_attestation","sign_citation":"https://pith.science/pith/4TBXGNY3KLYDQYHIM57ATSUEH2/action/citation_signature","submit_replication":"https://pith.science/pith/4TBXGNY3KLYDQYHIM57ATSUEH2/action/replication_record"}},"created_at":"2026-05-18T01:44:11.851866+00:00","updated_at":"2026-05-18T01:44:11.851866+00:00"}