  In this paper, for the purposes of information transmission and network error
correction simultaneously, three classes of important linear network codes in
network coding, linear multicast/broadcast/dispersion codes are generalized to
linear network error correction coding, i.e., linear network error correction
multicast/broadcast/dispersion codes. We further propose the (weakly, strongly)
extended Singleton bounds for these new classes of codes, and define the
optimal codes satisfying the corresponding Singleton bounds with equality,
which are called multicast/broadcast/dispersion MDS codes respectively. The
existence of such codes are proved by an algebraic method and one kind of
constructive algorithm is also proposed.
