{"paper":{"title":"The asymptotic behavior of automorphism groups of function fields over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chaoping Xing, Liming Ma","submitted_at":"2017-07-23T15:25:36Z","abstract_excerpt":"The purpose of this paper is to investigate the asymptotic behavior of automorphism groups of function fields when genus tends to infinity.\n  Motivated by applications in coding and cryptography, we consider the maximum size of abelian subgroups of the automorphism group $\\mbox{Aut}(F/\\mathbb{F}_q)$ in terms of genus ${g_F}$ for a function field $F$ over a finite field $\\mathbb{F}_q$. Although the whole group $\\mbox{Aut}(F/\\mathbb{F}_q)$ could have size $\\Omega({g_F}^4)$, the maximum size $m_F$ of abelian subgroups of the automorphism group $\\mbox{Aut}(F/\\mathbb{F}_q)$ is upper bounded by $4g_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07315","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"}