Asymptotically optimal rate for codes correcting partially localized burst errors

We consider block codes of length n on a q-ary channel with partially localised errors. The errors are supposed to occur in bursts, i.e. the errors are located in a block of consecutive positions. The encoder knows a set G, of g consecutive positions, where a burst of length b or less may occur. The decoder knows b and g but not G. The following relation holds, 0⩽b⩽g⩽n. We give an upper bound of the asymptotically optimal rate for burst error correction