{"paper":{"title":"Non Abelian Bent Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"cs.CR","authors_text":"Laurent Poinsot (LIPN)","submitted_at":"2010-12-18T10:15:05Z","abstract_excerpt":"Perfect nonlinear functions from a finite group $G$ to another one $H$ are those functions $f: G \\rightarrow H$ such that for all nonzero $\\alpha \\in G$, the derivative $d_{\\alpha}f: x \\mapsto f(\\alpha x) f(x)^{-1}$ is balanced. In the case where both $G$ and $H$ are Abelian groups, $f: G \\rightarrow H$ is perfect nonlinear if and only if $f$ is bent i.e for all nonprincipal character $\\chi$ of $H$, the (discrete) Fourier transform of $\\chi \\circ f$ has a constant magnitude equals to $|G|$. In this paper, using the theory of linear representations, we exhibit similar bentness-like characteriza"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4079","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"}