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Let $q$ be a prime power, let $m$ be an integer with $m \\geq 10$ and $m \\neq 12$, and set $u = \\lfloor m/4 \\rfloor$ and $t = \\lfloor (m-1)/3 \\rfloor$. For each integer $s$ with $u \\leq s < t$, we define$$\\delta = q^m - q^{m-1} - q^{m-1-u} - q^s - 1.$$We prove that the primitive narrow-sense BCH code with designed distance $\\delta$ has Bose distance $\\delta$ a"},"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":"2607.28741","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-07-30T18:01:50Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a3385f5e373b6691c8b8fa4ebeb34a6416bd59a12c1233ca03071b3a446aa7ff","abstract_canon_sha256":"aef7456cf5789c81387bbc655d274362b1e732da43423dd4b134fd5f16c003ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T00:12:32.578760Z","signature_b64":"BYgcuc+iRVrxRWsycz5dydAK8lPzJ4GNSe04v3gOQCodgWaJyACDmVdnedNfXtQlDFSIm4eYWs2sX76BDBfcBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51ee6875fac5d8c38b0b55271cbabb7c54faacd5e76dd75c954717b328316920","last_reissued_at":"2026-08-03T00:12:32.576417Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T00:12:32.576417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counterexamples to Charpin's Conjecture on BCH codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Maosheng Xiong, Run Zheng, Yaoran Yang, Yutong Zhang","submitted_at":"2026-07-30T18:01:50Z","abstract_excerpt":"Determining the exact minimum distance of BCH codes is a longstanding and challenging problem. 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