{"paper":{"title":"Semidefinite bounds for mixed binary/ternary codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.RT"],"primary_cat":"math.CO","authors_text":"Bart Litjens","submitted_at":"2016-06-22T12:50:08Z","abstract_excerpt":"For nonnegative integers $n_2, n_3$ and $d$, let $N(n_2,n_3,d)$ denote the maximum cardinality of a code of length $n_2+n_3$, with $n_2$ binary coordinates and $n_3$ ternary coordinates (in this order) and with minimum distance at least $d$. For a nonnegative integer $k$, let $\\mathcal{C}_k$ denote the collection of codes of cardinality at most $k$. For $D \\in \\mathcal{C}_k$, define $S(D) := \\{C \\in \\mathcal{C}_k \\mid D \\subseteq C, |D| +2|C\\setminus D| \\leq k\\}$. Then $N(n_2,n_3,d)$ is upper bounded by the maximum value of $\\sum_{v \\in [2]^{n_2}[3]^{n_3}}x(\\{v\\})$, where $x$ is a function $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06930","kind":"arxiv","version":2},"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"}