  In this paper, a linear $\ell$-intersection pair of codes is introduced as a
generalization of linear complementary pairs of codes.
  Two linear codes are said to be a linear $\ell$-intersection pair if their
intersection has dimension $\ell$.
  Characterizations and constructions of such pairs of codes are given in terms
of the corresponding generator and parity-check matrices.
  Linear $\ell$-intersection pairs of MDS codes over $\mathbb{F}_q$ of length
up to $q+1$ are given for all possible parameters.
  As an application, linear $\ell$-intersection pairs of codes are used to
construct entanglement-assisted quantum error correcting codes.
  This provides a large number of new MDS entanglement-assisted quantum error
correcting codes.
