Conventioally the decoding methods and the design of coset codes for burst synchronization and error detection have been based on the concept that slips occuring to the right or to the left with respect to a reference timing are corrected. In this paper we newly approach to the design of coset codes relying on the condition that only a single code word can exists in an observation interval, which provides an extentended view on the conventional approach. A theorem concerning the condition is presented. A combined burst synchronization and error detection system with maximum slip correction capability have been devised based on the theorem and a detection method is falsely accepted in the presented of channel errors. The false acceptance probabilities of the system are derived and its performance is analyzed through computer computation using the derived results.