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The burst-trapping error control technique developed by Tong  corrects both random and burst errors adaptively. A generalization of this scheme, called generalized burst trapping (GBT), is presented here. Generalized burst-trapping codes (GBTC) also correct both random and burst errors adaptively but, in addition, are capable of correcting random errors in the guard space following a correctable burst. This added capability is obtained at the expense of a longer guard space or a lower rate and a modest increase in complexity of implementation. Nevertheless, these codes are simple to encode and decode and, in particular, the storage-saving technique used with the original burst-trapping codes is directly applicable to the generalized codes. Also it is shown that at most one block of error propagation can occur if a simple and reasonable condition is met. Thus the generalized codes have better propagation properties than the original burst-trapping codes. This new error control technique is well suited to error correction on channels where it cannot be assumed that bursts are isolated events separated by error-free intervals. Thus, for example, this technique appears well suited to error correction on telephone facilities that incorporate multiple-level signaling.