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Here we determine $T(7)=16$, $T(8)=20$, and $T(9)=27$. For the latter case $n=9$ there also exist linear codes attaining the maximum possible cardinality $27$."},"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":"2310.13563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-10-20T15:03:44Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"504efee07716386c9ef36019b68b612b5d150ef23f8722d34005d6cbcd2ad195","abstract_canon_sha256":"cf60ce47b30a80ce4b63f62a48ef0d9d65376fdb9c0e205bee48b3146387e624"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:15:41.738716Z","signature_b64":"UJi/YrAypZWaxBDA3JJfsCsHKhJFG9fjZhPJOvwCEfoHYAjtexrbenlyenLCJ/y3FSdD1yIy+DrfabnC1yzjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1d6d826c115b265144acf7903b6f0e5932e0eaf307e160569869427578d0c6a","last_reissued_at":"2026-07-05T10:15:41.738225Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:15:41.738225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trifferent codes with small lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Sascha Kurz","submitted_at":"2023-10-20T15:03:44Z","abstract_excerpt":"A code $C \\subseteq \\{0, 1, 2\\}^n$ of length $n$ is called trifferent if for any three distinct elements of $C$ there exists a coordinate in which they all differ. 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