Issue No.04 - April (1973 vol.22)
H.F. Jordan , Departments of Computer Science and Electrical Engineering, University of Colorado
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.
Binomial distribution, linear recurring sequences, m-sequences, pseudorandom sequences, shift-register sequences.
H.F. Jordan, D.C.M. Wood, "On the Distribution of Sums of Successive Bits of Shift-Register Sequences", IEEE Transactions on Computers, vol.22, no. 4, pp. 400-408, April 1973, doi:10.1109/T-C.1973.223728