{"paper":{"title":"Large classes of permutation polynomials over $\\mathbb{F}_{q^2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dingyi Pei, Pingzhi Yuan, Yanbin Zheng","submitted_at":"2015-10-07T16:39:16Z","abstract_excerpt":"Permutation polynomials (PPs) of the form $(x^{q} -x + c)^{\\frac{q^2 -1}{3}+1} +x$ over $\\mathbb{F}_{q^2}$ were presented by Li, Helleseth and Tang [Finite Fields Appl. 22 (2013) 16--23]. 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 $a,b,c,u,v \\in \\mathbb{F}_{q^2}$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02021","kind":"arxiv","version":3},"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"}