{"paper":{"title":"Two types of permutation polynomials with special forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Dabin Zheng, Long Yu, Mu Yuan","submitted_at":"2018-05-28T14:00:35Z","abstract_excerpt":"Let $q$ be a power of a prime and $\\mathbb{F}_q$ be a finite field with $q$ elements. In this paper, we propose four families of infinite classes of permutation trinomials having the form $cx-x^s + x^{qs}$ over $\\mathbb{F}_{q^2}$, and investigate the relationship between this type of permutation polynomials with that of the form $(x^q-x+\\delta)^s+cx$. Based on this relation, many classes of permutation trinomials having the form $(x^q-x+\\delta)^s+cx$ without restriction on $\\delta$ over $\\mathbb{F}_{q^2}$ are derived from known permutation trinomials having the form $cx-x^s + x^{qs}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10926","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"}