.95). As a check, note that the results of Property R-6 reduce to those of the full period case R-5 when K = N. For comparison, consider a periodic sequence {xn} composed of N inde- pendent, identically distributed (i.i.d.) random variables, uniformly distrib- uted over the elements of GF(p), p prime. Furthermore, let {Zn} be the corresponding complex sequence determined by the usual mapping (5.80) to p-th roots of unity. Clearly the elements of {Zn} are i.i.d. random variables, uniformly distributed on the p-th roots of unity. Both the full-period and par- tial-period time-average autocorrelation functions of {Zn} are random vari- ables whose ensemble-average moments can be evaluated, using the independence assumption and the fact that E{zn}==0 (5.96) where E denotes the ensemble average operator. The first moment of the partial period correlation of {Zn} is easily shown to be T=0mod (5.97) Evaluation of the second moment of P(K,n,T) uses the fourth moment and T # 0 mod N (5.98) j and T # 0 mod N to yield P22(K, (5.99) 0 mod N. Statistical Properties of M-Sequences Comparisons of (5.97) and (5.99) for a random sequence with (5.91) and (5.92) for an m-seuence both indicate that when K << N, then the time- averaged mean and correlation values of an m-sequence are very close to the corresponding ensemble averages for a randomly chosen sequence. This fact and the balance properties of m-sequences are used to justify their approximation by a random sequence of bits in later analyses of SS system performance. Both the full-period and partial-period correlation computations have a particularly simple characterization when {bn} is a sequence of elements from GF(2) and {an} is a sequence of +1's and 1's. In this case when T # 0 mod N, = E(1)bn+/+r(+) = K - (5.100) where the weight wt(x) of a vector x denotes the number of non-zero ele- ments in X. Hence, PaaKKnn T) is a simple affine transformation of the weight of a K-tuple from {bn}, beginning at element index n + T'(T). This relation, a direct result of the shift-and-