On the Distribution of Sums of Successive Bits of Shift-Register Sequences
Harry F. Jordan, Derick Wood · IEEE Transactions on Computers · 1973
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.