{"paper":{"title":"The Existence of Minimal Logarithmic Signatures for some Finite Simple Unitary Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"A. R. Ashrafi, A. R. Rahimipour","submitted_at":"2019-08-12T12:50:19Z","abstract_excerpt":"The $MLS$ conjecture states that every finite simple group has a minimal logarithmic signature. The aim of this paper is proving the existence of a minimal logarithmic signature for some simple unitary groups $PSU_{n}(q)$. We report a gap in the proof of the main result of [H. Hong, L. Wang, Y. Yang, Minimal logarithmic signatures for the unitary group $U_n(q)$, \\textit{Des. Codes Cryptogr.} \\textbf{77} (1) (2015) 179--191] and present a new proof in some special cases of this result. As a consequence, the $MLS$ conjecture is still open."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04125","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04125/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}