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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1201.3291","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-16T15:50:31Z","cross_cats_sorted":[],"title_canon_sha256":"f3528d9d7992e875ff8c12e50e5745db708883b5025aacdd8d3bd3b2204f3fd3","abstract_canon_sha256":"5f01665111a30bd4d8c18f718373ad270d37ca032736ee5fbfe8dca7541dcf89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:31.713767Z","signature_b64":"39tDxjQIVy4AAPByW4ZZ4kcACX+i1IlaJX0OaDS4ZXdwU17XMA/Sflq0aXsULQsMDRFnxm4c5XZIn6Z29buhDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1377ca9a7a1b39eb368eba809bb4804702bfbd7c0969d2d7b57c31a509e0a6fb","last_reissued_at":"2026-05-18T04:04:31.713146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:31.713146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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). 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