In this note, necessary and sufficient conditions for the solvability of the disturbance-rejection problem with dynamic compensator (DRPDC), which has a time-varying state dimension, are given for Linear omega -periodic discrete-time systems without assuming that the order of dynamic compensator is equal to that of system plant. Further, the minimal order of dynamic compensator, which is necessary for the solution of the problem, is also investigated under the assumption that the disturbance map is independent of time k.