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Locally decodable codes and the failure of cotype for projective tensor products

Jop Briet 1 Assaf Naor 2 Oded Regev 3 
3 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique - ENS Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : It is shown that for every p is an element of (1, infinity) there exists a Banach space X of finite cotype such that the projective tensor product l(p) (circle times) over cap X fails to have finite cotype. More generally, if p(1); p(2); p(3) is an element of (1, infinity) satisfy 1/p(1) + 1/p(2) + 1/p(3) <= 1 then l(p1) (circle times) over capl(p2)(circle times) over capl(p3) does not have fi nite cotype. This is proved via a connection to the theory of locally decodable codes.
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Jop Briet, Assaf Naor, Oded Regev. Locally decodable codes and the failure of cotype for projective tensor products. Electronic Research Announcements in Mathematical Sciences, AIMS - American Institute of Mathematical Sciences, 2012, 19, pp.120-130. ⟨10.3934/era.2012.19.120⟩. ⟨hal-01111576⟩



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