{"paper":{"title":"New Constructions of Permutation Polynomials of the Form $x^rh\\left(x^{q-1}\\right)$ over $\\mathbb{F}_{q^2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Kangquan Li, Longjiang Qu, Qiang Wang","submitted_at":"2017-08-03T14:42:53Z","abstract_excerpt":"Permutation polynomials over finite fields have been studied extensively recently due to their wide applications in cryptography, coding theory, communication theory, among others. Recently, several authors have studied permutation trinomials of the form $x^rh\\left(x^{q-1}\\right)$ over $\\mathbb{F}_{q^2}$, where $q=2^k$, $h(x)=1+x^s+x^t$ and $r, s, t, k>0$ are integers. Their methods are essentially usage of a multiplicative version of AGW Criterion because they all transformed the problem of proving permutation polynomials over $\\mathbb{F}_{q^2}$ into that of showing the corresponding fraction"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01165","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"}