On Linear Perfect b -Symbol Codes over Finite Fields.

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 F q for e < 2 b and show that for 2 b ≤ e < 3 b , 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 F q using constacyclic codes. [ABSTRACT FROM AUTHOR]