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On the Distribution of Sums of Successive Bits of Shift-Register Sequences

By: Jordan, H.F.; Wood, D.C.M.;

1973 / IEEE

Description

This item was taken from the IEEE Periodical ' On the Distribution of Sums of Successive Bits of Shift-Register Sequences ' A formula is found for the distribution of the number of ones in a subsequence of a maximal-length shift-register sequence. The formula relates the distribution to the binomial distribution with probability 1/2 with a difference that depends on the structure of the set of linear recurrences satisfied by the sequence. Considerations are discussed that aid in the choice of a shift register to be used in generating an approximately binomially distributed random variable.