  Error-correcting pairs were introduced in 1988 by R. Pellikaan, and were
found independently by R. K\"otter (1992), as a general algebraic method of
decoding linear codes. These pairs exist for several classes of codes. However
little or no study has been made for characterizing those codes. This article
is an attempt to fill the vacuum left by the literature concerning this
subject. Since every linear code is contained in an MDS code of the same
minimum distance over some finite field extension we have focused our study on
the class of MDS codes.
  Our main result states that an MDS code of minimum distance $2t+1$ has a
$t$-ECP if and only if it is a generalized Reed-Solomon code. A second proof is
given using recent results Mirandola and Z\'emor (2015) on the Schur product of
codes.
