{"paper":{"title":"On the characterization of minimal value set polynomials","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Herivelto Borges, Ricardo Concei\\c{c}\\~ao","submitted_at":"2011-08-09T03:32:38Z","abstract_excerpt":"We give an explicit characterization of all minimal value set polynomials in $\\F_q[x]$ whose set of values is a subfield $\\F_{q'}$ of $\\F_{q}$. We show that the set of such polynomials, together with the constants of $\\F_{q'}$, is an $\\F_{q'}$-vector space of dimension $2^{[\\F_{q}:\\F_{q'}]}$. Our approach not only provides the exact number of such polynomials, but also yields a construction of new examples of minimal value set polynomials for some other fixed value sets. In the latter case, we also derive a non-trivial lower bound for the number of such polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1852","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"}