{"paper":{"title":"On the code generated by the incidence matrix of points and k-spaces in PG(n, q) and its dual","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Geertrui Van de Voorde, Leo Storme, Michel Lavrauw","submitted_at":"2012-01-16T15:50:31Z","abstract_excerpt":"In this paper, we study the p-ary linear code Ck(n, q), q = ph, p prime, h >= 1, generated by the incidence matrix of points and k-dimensional spaces in PG(n, q). For k >= n/2, we link codewords of Ck(n, q)\\Ck(n, q) of weight smaller than 2q^k to k-blocking sets. We first prove that such a k-blocking set is uniquely reducible to a minimal k-blocking set, and exclude all codewords arising from small linear k-blocking sets. For k < n/2, we present counterexamples to lemmas valid for k >= n/2. Next, we study the dual code of Ck(n, q) and present a lower bound on the weight of the codewords, hence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3291","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"}