{"paper":{"title":"Codes and caps from orthogonal Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CO","math.IT"],"primary_cat":"math.AG","authors_text":"Ilaria Cardinali, Luca Giuzzi","submitted_at":"2013-03-22T14:56:42Z","abstract_excerpt":"In this paper we investigate linear error correcting codes and projective caps related to the Grassmann embedding $\\varepsilon_k^{gr}$ of an orthogonal Grassmannian $\\Delta_k$. In particular, we determine some of the parameters of the codes arising from the projective system determined by $\\varepsilon_k^{gr}(\\Delta_k)$. We also study special sets of points of $\\Delta_k$ which are met by any line of $\\Delta_k$ in at most 2 points and we show that their image under the Grassmann embedding $\\varepsilon_k^{gr}$ is a projective cap."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5636","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"}