Spectrum of sizes for perfect burst deletion-correcting codes

Perfect deletion-correcting codes of the same length over the same alphabet can have different sizes. The interesting problem of determining the possible sizes of perfect deletion-correcting codes has previously been studied. In this paper, we study the corresponding problem for burst deletion-correcting codes. We completely determine the spectrum of sizes for perfect burst deletion-correcting codes for certain classes of parameters and also construct new classes of perfect deletion-correcting codes.