{"paper":{"title":"On the 2-ranks of a class of unitals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rocco Trombetti, Yue Zhou","submitted_at":"2015-10-12T15:37:48Z","abstract_excerpt":"Let $U_\\theta$ be a unital defined in a shift plane of odd order $q^2$, which are constructed recently by the authors. In particular, when the shift plane is desarguesian, $U_\\theta$ is a special Buekenhout-Metz unital formed by a union of ovals. We investigate the dimensions of the binary codes derived from $U_\\theta$.\n  By using Kloosterman sums, we obtain a new lower bound on the aforementioned dimensions which improves the result obtained by Leung and Xiang in 2009. In particular, for $q=3^m$, this new lower bound equals $\\frac{2}{3}(q^3+q^2-2q)-1$ for even $m$ and $\\frac{2}{3}(q^3+q^2+q)-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03340","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"}