{"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 $d$. We consider the following upper bound on $A_q(n,d)$. For any $k$, let $\\CC_k$ be the collection of codes of cardinality at most $k$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02531","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}