In this letter, we construct two rate efficient codes of length $n$ named as marker-MDS and marker-SVT codes which correct a burst of deletions/insertions of length $b$ (error-free decoding), where $b$ is not necessarily fixed as a constant but is proportional to $n$ , i.e., $b=tn$ , $0\lt t\lt 1$ . Both of these two codes consist of binary marker codes which are employed to locate the burst of deletions/insertions. Also, the marker-MDS and marker-SVT codes consist of the maximum distance separable (MDS) codes and shifted Varshamov-Tenengol’ts (SVT) codes, respectively, which are responsible for correcting erasures caused in the synchronization stage. Both the theoretical and simulation results verify that the constructed marker-MDS and marker-SVT codes provide the higher code rate than the existing run-length limited Varshamov-Tenengol’ts shifted Varshamov-Tenengol’ts (RLLVT-SVT) codes if $n$ is not smaller than a lower bound $f(t)$ which is determined by $t$ .