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

Jop T. Brië; Assaf Naor; Oded Regev

doi:10.3934/era.2012.19.120

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

Jop T. Brië, Assaf Naor, Oded Regev

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

It is shown that for every p ε (1, ∞) there exists a Banach space X of finite cotype such that the projective tensor product ℓ_pX fails to have finite cotype. More generally, if p₁, p2,p₃ ε (1,∞) satisfy 1/p1+1/p2+1/p3 ≤ 1 then l_p1l_p2p3 does not have finite cotype. This is proved via a connection to the theory of locally decodable codes.

Original language	English (US)
Pages (from-to)	120-130
Number of pages	11
Journal	Electronic Research Announcements in Mathematical Sciences
Volume	19
DOIs	https://doi.org/10.3934/era.2012.19.120
State	Published - 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Cotype
Locally decodable codes
Projective tensor product

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10.3934/era.2012.19.120

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abstract = "It is shown that for every p ε (1, ∞) there exists a Banach space X of finite cotype such that the projective tensor product ℓpX fails to have finite cotype. More generally, if p1, p2,p3 ε (1,∞) satisfy 1/p1+1/p2+1/p3 ≤ 1 then lp1lp2p3 does not have finite cotype. This is proved via a connection to the theory of locally decodable codes.",

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AU - Naor, Assaf

AU - Regev, Oded

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N2 - It is shown that for every p ε (1, ∞) there exists a Banach space X of finite cotype such that the projective tensor product ℓpX fails to have finite cotype. More generally, if p1, p2,p3 ε (1,∞) satisfy 1/p1+1/p2+1/p3 ≤ 1 then lp1lp2p3 does not have finite cotype. This is proved via a connection to the theory of locally decodable codes.

AB - It is shown that for every p ε (1, ∞) there exists a Banach space X of finite cotype such that the projective tensor product ℓpX fails to have finite cotype. More generally, if p1, p2,p3 ε (1,∞) satisfy 1/p1+1/p2+1/p3 ≤ 1 then lp1lp2p3 does not have finite cotype. This is proved via a connection to the theory of locally decodable codes.

KW - Cotype

KW - Locally decodable codes

KW - Projective tensor product

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JO - Electronic Research Announcements in Mathematical Sciences

JF - Electronic Research Announcements in Mathematical Sciences

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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