{"paper":{"title":"A general construction of permutation polynomials of the form $ (x^{2^m}+x+\\delta)^{i(2^m-1)+1}+x$ over $\\F_{2^{2m}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Baofeng Wu, Libo Wang","submitted_at":"2017-12-21T16:35:39Z","abstract_excerpt":"Recently, there has been a lot of work on constructions of permutation polynomials of the form $(x^{2^m}+x+\\delta)^{s}+x$ over the finite field $\\F_{2^{2m}}$, especially in the case when $s$ is of the form $s=i(2^m-1)+1$ (Niho exponent). In this paper, we further investigate permutation polynomials with this form. Instead of seeking for sporadic constructions of the parameter $i$, we give a general sufficient condition on $i$ such that $(x^{2^m}+x+\\delta)^{i(2^m-1)+1}+x$ permutes $\\F_{2^{2m}}$, that is, $(2^k+1)i \\equiv 1 ~\\textrm{or}~ 2^k~(\\textrm{mod}~ 2^m+1)$, where $1 \\leq k \\leq m-1$ is a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08066","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"}