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More recently, we have constructed PPs of the form $(x^{q} +bx + c)^{\\frac{q^2 -1}{d}+1} -bx$ over $\\mathbb{F}_{q^2}$, where $d=2, 3, 4, 6$ [Finite Fields Appl. 35 (2015) 215--230]. In this paper we concentrate our efforts on the PPs of more general form\n  \\[\n  f(x)=(ax^{q} +bx +c)^r \\phi((ax^{q} +bx +c)^{(q^2 -1)/d}) +ux^{q} +vx~~\\text{over $\\mathbb{F}_{q^2}$},\n  \\]\n  where $a,b,c,u,v \\in \\mathbb{F}_{q^2}$, ","authors_text":"Dingyi Pei, Pingzhi Yuan, Yanbin Zheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-07T16:39:16Z","title":"Large classes of permutation polynomials over $\\mathbb{F}_{q^2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02021","kind":"arxiv","version":3},"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:f443fdcf6efcb3f5a1c6f7ec3105a8ef4002f3a18acce7192ed054e93c3dce7a","target":"record","created_at":"2026-05-17T23:57:59Z","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":"62d8593f94aa0aa57a13bd15f12ffd4b1d8bf88b47913d5b3350efbb0b142275","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-07T16:39:16Z","title_canon_sha256":"376f70bb7d53c6665569107b53ce472524b488a022924bb075c9dcfbd088184e"},"schema_version":"1.0","source":{"id":"1510.02021","kind":"arxiv","version":3}},"canonical_sha256":"6f5a66fb56c99773ac25c3dc6700da89d6ddfa5c097903d1b29f14062a7c20df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f5a66fb56c99773ac25c3dc6700da89d6ddfa5c097903d1b29f14062a7c20df","first_computed_at":"2026-05-17T23:57:59.981169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:59.981169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y+7K4XmjN0j6nD0tf65+cPAhJLyorWFpjIy9SYJ5mJEk9i/Q393dVHiz6bkFStp49ppdKf0jbwmP/vhHs37ADg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:59.981582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.02021","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f443fdcf6efcb3f5a1c6f7ec3105a8ef4002f3a18acce7192ed054e93c3dce7a","sha256:076eb1802851ca27f65f3c3436c938c723304db351e95e892f3c2f642fff9b57"],"state_sha256":"24c40aa3518d69914312c580a301d8553d4a3d1986fe98211891ae5b688a8703"}