Abstract
Motivated by the application of high-density data storage technologies, Cassuto and Blaum introduced codes for symbol-pair read channels in 2011, and Yaakobi et al. generalized the coding framework to that for b-symbol read channels where b≥2 in 2016. In this paper, we establish a b-sphere-packing bound and present a recurrence relationship for the b-weight enumerator. We determine all parameters of linear perfect b-symbol e-error-correcting codes over Fq for e<2b and show that for 2b≤e<3b, there exist at most finite such codes for a given b, e, and q. We construct a family of linear perfect b-symbol b-error-correcting codes over Fq using constacyclic codes.
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