In the concept of localized burst errors, it is assumed that the encoder knows where the burst may occur. On the other hand, the decoder does not have this extra information. It has been proved that the localized-burst-error-correcting-code will produce a higher coderate than any other conventional burst-error-correcting-code. The goal of this thesis is to construct a new code that can correct localized burst errors. In both cases, single and multiple localized bursts, the coderate is indeed improved. Furthermore, a new concept of partially localized bursts will also be introduced.