A class of asymptotically optimal burst-correcting codes that are closely related to the Fire codes is defined. The codes are quasi-cyclic as defined by Townsend and Weldon. However, decoding can be accomplished with a very simple algorithm similar to that used for cyclic burst-correcting codes. It is shown that these codes are equivalent to certain Reed-Solomon codes. From this it follows that such Reed-Solomon codes can be easily encoded and decoded without any computations in an extension field.

The iterative algorithm for decoding binary BCH codes presented by Berlekamp and, in an alternative form, by Massey is modified to eliminate inversion. Because inversion in a finite field is time consuming and requires relatively complex circuitry, this new algorithm should he useful in practical applications of multiple-error-correcting binary BCH codes.

The burst-trapping error control technique developed by Tong [1] 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.