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Presented here is a practical automatic error-correcting system that may be applied to many data transmission problems. It is particularly suited to the correction of bursts of errors and so may be applied to the problem of the transmission of data over telephone networks. The attractive feature of the system is its remarkable simplicity from the point of view of implementation. It is so simple that it can readily be incorporated into much existing equipment. In the system, messages are transmitted in blocks and each block is coded separately. The codes used within the blocks are cyclic codes. This means that coders and decoders employ linear feedback shift registers to form check digits and to correct errors. The basic ideas are presented in terms of the hardware components to which the system gives rise and analyzed afterwards in terms of mathematics so that it is easy for the engineer to see, at once, what is involved. The theory usually applies to binary messages in which data is transmitted serially. However, an extension is included which shows how the same ideas may be applied to binary codes in which information is sent in parallel.