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

@article{Brit2012LocallyDC,
title={Locally decodable codes and the failure of cotype for projective tensor products},
author={J. Bri{\"e}t and A. Naor and O. Regev},
journal={ArXiv},
year={2012},
volume={abs/1208.0539}
}
• Published 2012
• Mathematics, Computer Science
• ArXiv
• 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 $l_p\hat\otimes X$ 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 $l_{p_1}\hat\otimes l_{p_2} \hat\otimes l_{p_3}$ does not have finite cotype. This is proved via a connection to the theory of locally decodable codes.