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

Jop T. Brië, Assaf Naor, Oded Regev

Research output: Contribution to journalArticle

8 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 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.

Original languageEnglish (US)
Pages (from-to)120-130
Number of pages11
JournalElectronic Research Announcements in Mathematical Sciences
Volume19
DOIs
StatePublished - 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Cotype
  • Locally decodable codes
  • Projective tensor product

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