{"paper":{"title":"Graphs of Vectorial Plateaued Functions as Difference Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ay\\c{c}a \\c{C}e\\c{s}melio\\u{g}lu, Oktay Olmez","submitted_at":"2018-07-30T05:52:56Z","abstract_excerpt":"A function $F:\\mathbb{F}_{p^n}\\rightarrow \\mathbb{F}_{p^m},$ is a vectorial $s$-plateaued function if for each component function $F_{b}(\\mu)=Tr_n(\\alpha F(x)), b\\in \\mathbb{F}_{p^m}^*$ and $\\mu \\in \\mathbb{F}_{p^n}$, the Walsh transform value $|\\widehat{F_{b}}(\\mu)|$ is either $0$ or $ p^{\\frac{n+s}{2}}$. In this paper, we explore the relation between (vectorial) $s$-plateaued functions and partial geometric difference sets. Moreover, we establish the link between three-valued cross-correlation of $p$-ary sequences and vectorial $s$-plateaued functions. Using this link, we provide a partition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11181","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"}