The autocorrelation structure of Tausworthe pseudorandom number generators

An algorithm for determining the autocorrelation structure of a new sequence generated from an original sequence by proper decimation (a shift with each q-th term of the original sequence used) is presented, once autocorrelations for any repeating number sequence are known. The autocorrelation structure of the Tausworthe random number generator (RNG), based on proper decimation by q, is accepted as a RNG structure in which a proper decimation generates a long interval over which autocorrelations are small for all shifts. It is shown that if L bits of an N-bit Tausworthe RNG are L-bit binary numbers, L + 1 levels of correlation will exist, and L levels of correlation will each occur twice per RNG cycle length.