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Then $A_q(n,d)$ is at most the maximum value of $\\sum_{v\\in[q]^n}x(\\{v\\})$, where $x$ is a function $\\CC_4\\to R_+$ such that $x(\\emptyset)=1$ and $x(C)=0$ if $C$ has minimum distance less than $d$, and such that the $\\CC_2\\times\\CC_2$ matrix $(x(C\\cup C'))_{C,C'\\in\\CC_2}$ is positiv"},"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":"1602.02531","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-08T11:30:19Z","cross_cats_sorted":["math.OC","math.RT"],"title_canon_sha256":"0427e6e0381e7c33d576ddbced15c7c8ad4d19c43280170ba1c24490b1717def","abstract_canon_sha256":"b86da2eb9c099a1cd402adcd3a001541b17a6de5f4e594f75d52c7e8d9756db9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:58.087978Z","signature_b64":"ztzyuhYmMv/T6SRUfgPy2KxS7H7Mdp6r8jPqkv6ffEQtMtuRnVKmzxA1JYeLJCeUuo8geAGHpy73z3fbnyf3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4155cfc465a6b9d26633c1fdaae59a878795b043684210797666c19841c1f3e6","last_reissued_at":"2026-05-18T00:08:58.087294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:58.087294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semidefinite bounds for nonbinary codes based on quadruples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.RT"],"primary_cat":"math.CO","authors_text":"Alexander Schrijver, Bart Litjens, Sven Polak","submitted_at":"2016-02-08T11:30:19Z","abstract_excerpt":"For nonnegative integers $q,n,d$, let $A_q(n,d)$ denote the maximum cardinality of a code of length $n$ over an alphabet $[q]$ with $q$ letters and with minimum distance at least $d$. 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