{"paper":{"title":"Proofs of Two Conjectures On the Dimensions of Binary Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Junhua Wu","submitted_at":"2010-01-28T01:20:06Z","abstract_excerpt":"Let $\\mathcal{L}$ and $\\mathcal{L}_0$ be the binary codes generated by the column $\\mathbb{F}_2$-null space of the incidence matrix of external points versus passant lines and internal points versus secant lines with respect to a conic in $PG(2, q)$, respectively. We confirm the conjectures on the dimensions of $\\mathcal{L}$ and $\\mathcal{L}_0$ using methods from both finite geometry and modular representation theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.5077","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"}