{"paper":{"title":"Locally decodable codes and the failure of cotype for projective tensor products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.FA","authors_text":"Assaf Naor, Jop Briet, Oded Regev","submitted_at":"2012-08-02T16:48:50Z","abstract_excerpt":"It is shown that for every $p\\in (1,\\infty)$ there exists a Banach space $X$ of finite cotype such that the projective tensor product $\\ell_p\\tp X$ fails to have finite cotype. More generally, if $p_1,p_2,p_3\\in (1,\\infty)$ satisfy $\\frac{1}{p_1}+\\frac{1}{p_2}+\\frac{1}{p_3}\\le 1$ then $\\ell_{p_1}\\tp\\ell_{p_2}\\tp\\ell_{p_3}$ does not have finite cotype. This is a proved via a connection to the theory of locally decodable codes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0539","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"}