{"paper":{"title":"Frobenius linear translators giving rise to new infinite classes of permutations and bent functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AC","authors_text":"Amela Muratovi\\'c-Ribi\\'c, Enes Pasalic, Nastja Cepak","submitted_at":"2018-01-25T15:52:59Z","abstract_excerpt":"We show the existence of many infinite classes of permutations over finite fields and bent functions by extending the notion of linear translators, introduced by Kyureghyan [12]. We call these translators Frobenius translators since the derivatives of $f : F_{p^n} \\rightarrow F_{p^k}$, where $n = rk$, are of the form $f(x + u\\phi) - f(x) = u^{p^i}b$, for a fixed $b \\in F_{p^k}$ and all $u \\in F_{p^k}$, rather than considering the standard case corresponding to $i = 0$. This considerably extends a rather rare family {f} admitting linear translators of the above form. Furthermore, we solve a few"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08460","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"}