A mixed upper bound on the maximum size of codes for multiple burst error correction and detection

We derive an upper bound on the size of a block code with prescribed burst-error-correcting capability combining those two ideas underlying the generalized Singleton and sphere-packing bounds. The two ideas are puncturing and sphere-packing. We use the burst metric defined by Gabidulin [1], which is suitable for burst error correction and detection. It is demonstrated that the proposed bound improves previously known ones for finite code-length, when minimum distance is greater than 3, as well as in the asymptotic forms.