{"paper":{"title":"Essential dimension and error-correcting codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Athena Nguyen, Shane Cernele, Zinovy Reichstein","submitted_at":"2014-06-11T16:17:03Z","abstract_excerpt":"One of the important open problems in the theory of central simple algebras is to compute the essential dimension of $\\operatorname{GL}_n/\\mu_m$, i.e., the essential dimension of a generic division algebra of degree $n$ and exponent dividing $m$. In this paper we study the essential dimension of groups of the form \\[ G=(\\operatorname{GL}_{n_1} \\times \\dots \\times \\operatorname{GL}_{n_r})/C \\, , \\] where $C$ is a central subgroup of $\\operatorname{GL}_{n_1} \\times \\dots \\times \\operatorname{GL}_{n_r}$. Equivalently, we are interested in the essential dimension of a generic $r$-tuple $(A_1, \\dot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2953","kind":"arxiv","version":2},"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"}