Subsequences of Pseudorandom Sequences

The properties of subsequences of long
m
sequences are studied using the moments of the subsequence weight distributions. These moments are shown to be an aid for selecting good
m
sequences for correlation-detection problems. In particular, the first four moments are described in detail for subsequence lengths
M \leq 100
digits for six different
m
sequences. Two simple algorithms are described for determining the third and fourth moments. An algorithm for calculating the fourth moment and a detailed description of this moment for the six
m
sequences are presented in this paper. Using the moments, a relationship is shown between the subsequences of the pseudorandom binary sequence and subsequences composed of random binary digits. Estimates for the moments of the subsequence weight distribution are obtained by sampling the
m
sequence. A statistical analysis of these results is presented.