{"paper":{"title":"New results on permutation polynomials over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Guoyou Qian, Shaofang Hong, Xiaoer Qin","submitted_at":"2014-03-24T15:47:58Z","abstract_excerpt":"In this paper, we get several new results on permutation polynomials over finite fields. First, by using the linear translator, we construct permutation polynomials of the forms $L(x)+\\sum_{j=1}^k \\gamma_jh_j(f_j(x))$ and $x+\\sum_{j=1}^k\\gamma_jf_j(x)$. These generalize the results obtained by Kyureghyan in 2011. Consequently, we characterize permutation polynomials of the form $L(x)+\\sum_{i=1} ^l\\gamma_i {\\rm Tr}_{{\\bf F}_{q^m}/{\\bf F}_{q}}(h_i(x))$, which extends a theorem of Charpin and Kyureghyan obtained in 2009."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6012","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"}