Maximum distance separable codes for b-symbol read channels

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 bdistance. 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.