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The codes discussed here, due to E. N. Gilbert, are capable of detecting and correcting certain bursts, i.e., errors which occur in clusters. In particular, it is shown that Gilbert's burst-correcting cedes have capabilities beyond those previously recognized. D. A. Huffman's graph-code formulation is used, which greatly facilitates the appreciation of the results. A cyclic code formulation is also given, and certain Gilbert codes are seen to be Fire codes.