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The Friedman and Fon-Der-Flaass bounds on the correlation immunity order say that such a function must satisfy $t\\le 2n/3-1$; moreover, the $(2n/3-1)$-resilient $(n,2)$-functions correspond to the equitable partitions of the $n$-cube with the quotient matrix $[[0,r,r,r],[r,0,r,r],[r,r,0,r],[r,r,r,0]]$, $r=n/3$. We suggest constructions of such functions and corresponding pa"},"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":"1902.00022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-31T19:00:03Z","cross_cats_sorted":["cs.DM","cs.IT","math.IT"],"title_canon_sha256":"b554e6a5dc7d6afb4c2ca17bb5a23efded81ab77746091c9e9ef146f3bdc0d6d","abstract_canon_sha256":"2e0407d3b595d516f0bdff494525efe41a84755b842265f3856cbbc5c374de9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:01.560938Z","signature_b64":"zLAvrBGDDzz73REgBNYL8El1Qw9Rwrwlp5olfbrCuFruNK4hV7M9bmsYZDfUcwIIzit7qxtX42J+tCba08isCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdec351da7e993584dbb324c5ee3b643c10006e797a95d9b3179181f70c5eb81","last_reissued_at":"2026-05-17T23:55:01.560548Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:01.560548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $(2n/3-1)$-resilient $(n,2)$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Denis S. Krotov (Sobolev Institute of Mathematics, Novosibirsk, Russia)","submitted_at":"2019-01-31T19:00:03Z","abstract_excerpt":"A $\\{00,01,10,11\\}$-valued function on the vertices of the $n$-cube is called a $t$-resilient $(n,2)$-function if it has the same number of $00$s, $01$s, $10$s and $11$s among the vertices of every subcube of dimension $t$. The Friedman and Fon-Der-Flaass bounds on the correlation immunity order say that such a function must satisfy $t\\le 2n/3-1$; moreover, the $(2n/3-1)$-resilient $(n,2)$-functions correspond to the equitable partitions of the $n$-cube with the quotient matrix $[[0,r,r,r],[r,0,r,r],[r,r,0,r],[r,r,r,0]]$, $r=n/3$. 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