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A partition $P^n= \\{H_0,H_1+e_1,\\ldots,H_n+e_n\\}$ of $F^n$ into cosets of Hamming codes $H_0,H_1,\\ldots,H_n$ of length $n$ is said to be uniform if the intersection of any two codes $H_i$ and $H_j$, $i,j\\in \\{0,1,\\ldots,n \\}$ is constant, here $e_i$ is a binary vector in $F^n$ of weight $1$ with one in the $i$th coordinate position.\n  For any $n=2^m-1$, $m>4$ we found a class of nonequivalent $2$-transitive uniform partitions of $F^n$ into cosets o"},"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":"1904.01282","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-04-02T08:40:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"267c089fac36902bb6662c42abf634bfc6ddd71ac5420d81e8176f6780b5141c","abstract_canon_sha256":"641264f9fd9c5e8b2dad855f16a59d0132d382d2411bd978820c30703aef45de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:35.280330Z","signature_b64":"n8GkgvUaKvRfy3FXehRzzwqP3oL+v6odMvsdYCwuUxN2PfpzFKwDrxmudzil+pZL1bNF22bIhiJNE56WGpKsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78d99e6166933147d7a002838174b82da0d5a42b3941f496f18c3a3723ffe4e6","last_reissued_at":"2026-05-17T23:49:35.279407Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:35.279407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On transitive uniform partitions of F^n into binary Hamming codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Faina I. 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