On Minimum Expected Length Prefix Codes Satisfying a (d, k) Runlength-Limited Constraint

A prefix code X is said to satisfy the (d, k) runlength- limited (RLL) constraint if all the possible concatenations of the codewords of X satisfy the (d, k) RLL constraint. In this paper, the problem of constructing a minimum expected length prefix code satisfying the (d, k) RLL constraint is studied for certain (d, k) pairs. The question of maximality, with maximality defined relative to the RLL constraint, of these optimal prefix codes is also taken up and answered for some cases