{"paper":{"title":"Idempotent and p-potent quadratic functions: Distribution of nonlinearity and co-dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alev Topuzoglu, Nurdag\\\"ul Anbar, Wilfried Meidl","submitted_at":"2016-03-15T13:44:40Z","abstract_excerpt":"The Walsh transform $\\widehat{Q}$ of a quadratic function $Q:F_{p^n}\\rightarrow F_p$ satisfies $|\\widehat{Q}(b)| \\in \\{0,p^{\\frac{n+s}{2}}\\}$ for all $b\\in F_{p^n}$, where $0\\le s\\le n-1$ is an integer depending on $Q$. In this article, we study the following three classes of quadratic functions of wide interest. The class $\\mathcal{C}_1$ is defined for arbitrary $n$ as $\\mathcal{C}_1 = \\{Q(x) = Tr(\\sum_{i=1}^{\\lfloor (n-1)/2\\rfloor}a_ix^{2^i+1})\\;:\\; a_i \\in F_2\\}$, and the larger class $\\mathcal{C}_2$ is defined for even $n$ as $\\mathcal{C}_2 = \\{Q(x) = Tr(\\sum_{i=1}^{(n/2)-1}a_ix^{2^i+1}) +"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04685","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"}