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Codes have been discussed recently in connection with signal compression and noise reduction in communication theory, and they are here defined as transformations between two time series of discrete symbols. The electronic apparatus which performs the transformation, or any part of the apparatus, can be described by a linear graph which represents transitions between different memory-states. It will be shown how these graphs can be used to systematically classify codes, combine different blocks of apparatus, examine synchronism of decoding apparatus, etc. Linear graphs have been studied as mathematical systems in connection with topology, Markov chains, and electrical network theory; hence there is already much theory which might be profitably applied to communication problems.