The difference set design of Gordon, Mills, and Welch (GMW) is adapted for use as a pseudorandom number generator. Statistical properties of the generated binary sequences, including periodic correlation, linear span, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> -tuple statistics, are derived. One mechanization of a GMW sequence generator is suggested, and the number of sequences that can be generated with a fixed number of shift-register stages and read-only memory (ROM) size is evaluated.
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Scholtz et al. (1984) studied this question.
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