  Recently, Yaakobi et al. introduced codes for $b$-symbol read channels, where
the read operation is performed as a consecutive sequence of $b>2$ symbols. In
this paper, we establish a Singleton-type bound on $b$-symbol codes. Codes
meeting the Singleton-type bound are called maximum distance separable (MDS)
codes, and they are optimal in the sense they attain the maximal minimum
$b$-distance. Based on projective geometry and constacyclic codes, we construct
new families of linear MDS $b$-symbol codes over finite fields. And in some
sense, we completely determine the existence of linear MDS $b$-symbol codes
over finite fields for certain parameters.
