  Ben-Sasson and Sudan (RSA 2006) showed that repeated tensor products of
linear codes with a very large distance are locally testable. Due to the
requirement of a very large distance the associated tensor products could be
applied only over sufficiently large fields. Then Meir (SICOMP 2009) used this
result (as a black box) to present a combinatorial construction of locally
testable codes that match best known parameters. As a consequence, this
construction was obtained over sufficiently large fields.
  In this paper we improve the result of Ben-Sasson and Sudan and show that for
\emph{any} linear codes the associated tensor products are locally testable.
Consequently, the construction of Meir can be taken over any field, including
the binary field.
  Moreover, a combination of our result with the result of Spielman (IEEE IT,
1996) implies a construction of linear codes (over any field) that combine the
following properties: have constant rate and constant relative distance; have
blocklength $n$ and testable with $n^{\epsilon}$ queries, for any constant
$\epsilon > 0$; linear time encodable and linear-time decodable from a constant
fraction of errors.
  Furthermore, a combination of our result with the result of Guruswami et al.
(STOC 2009) implies a similar corollary regarding the list-decodable codes.
