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

Jop Briet 1 Assaf Naor 2 Oded Regev 3
1 CWI - Centrum Wiskunde & Informatica
2 CIMS - Courant Institute of Mathematical Sciences [New York]
3 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, 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.
Keywords : cotype projective tensor product locally decodable codes
Type de document :
Article dans une revue
Electronic Research Announcements in Mathematical Sciences, American Institute of Mathematical Sciences, 2012, 19, pp.120-130. 〈10.3934/era.2012.19.120〉
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https://hal.inria.fr/hal-01111576
Contributeur : Brigitte Briot <>
Soumis le : vendredi 30 janvier 2015 - 15:49:56
Dernière modification le : vendredi 29 juin 2018 - 09:41:25

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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, American Institute of Mathematical Sciences, 2012, 19, pp.120-130. 〈10.3934/era.2012.19.120〉. 〈hal-01111576〉

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