, l are constrained by the relation k(k - 1) = 1(u - 1 (5.176) It is easily verified that modulo V addition of a constant to each element of a difference set yields a new difference set with the same parameters. The complement {0, 1, , V -1}-2 - of a v, k, l difference set D is a v*, k*, 1* Pseudonoise Generators difference set D* with V* = v, 1. (5.177) The incidence vector b of a difference set has elements defined by (5.178) for 0 < n < V. The sequence {bn} constructed by extending the incidence vec- tor periodically with period V has a two-level periodic correlation function Pbb(T) given by T = 0 mod u (5.179) T # 0 mod v. Conversely, if a periodic binary (0 or 1) sequence {bn} has two-level periodic correlation function, then one period of {bn} is the index vector of a differ- ence set. A binary roots-of-unity sequence {an}, based on the difference set D can be constructed via the relation an = =(-1)' = 1 - 2b,, (5.180) bn being 0 or 1. The periodic correlation function Paa(T) of the sequence {an} also is two valued, being = T=0modv T#0 mod V. (5.181) Any binary (+1 or -1) sequence with two-level periodic correlation can be related to the incidence matrix of a difference set by (5.180). One period of an m-sequence, generated by an M-stage shift register, is the incidence vector for a difference set with parameters (5.181) and, complementing this set gives another difference set with parameters V* 2M - 1, k* = 2M-1 = - 1, 1* = 2M-2 - 1. (5.183) These difference sets, corresponding to m-sequences, are called Singer sets, and were developed as a result of work in finite projective geometry [27]. Turyn [68] and Baumert [26] survey the known difference set designs. Decimation of any of the resulting sequences may produce a class of poten- tially interesting pseudorandom sequences. The sequences to be discussed next are one such class which has many nice attributes. Non-Linear Feed-Forward Logic 5.6.4 GMW Sequences Gordon, Mills, and Welch (GMW) [28] have generalized the structure of Singer sets, thereby creating 