sequences produced by this generator has an absolute correlation measure Pmax of 65. The linear span L of a bent sequence can be bounded by Key's technique (5.172) to give L=E(4) (5.347) where D is the order of the nonlinearity employed in a d-stage register design, D presumably taking on the maximum allowed value d/4 (when d 8) as determined by the choice of arbitrary nonlinearity g() (see (5.320)). Key's bound is not tight in this case, the intuitive reason for this being the fact that the nonlinearity is imposed on a lower dimensional sub- space. The following theorem provides upper and lower bounds on the lin- ear span of a well-designed bent sequence. THEOREM 5.23 [46]. Let L denote the maximum-achievable linear span of bent sequences produced by maximal-order (d/4) NLFFL functions oper- ating on a d-stage LFSR with d at least 8 and divisible by 4. Then L can be upper- and lower-bounded as follows: (5.348a) (5.348b) Shift Register with Characteristic Polynomial 12 +2 6 +1 4 + (Basis) Contents ~ X Basis Reduction Matrix M (for Balance) Output Sequence Sequence (x)+s'x Bent Function Selector q. Switch Settings Figure 5.16. Typical bent sequence generator. Connections correspond to Example 5.16. Direct-Sequence Multiple-Access Designs Table 5.18 Bounds on the maximum linear span of bent function sequences employing d-stage generators. lower bound upper bound 10334 14204 76804 114512 577098 938004 The term (d/2)24/4 tends to dominate the lower bound and, therefore, may be used as a conservative estimate of the achievable linear span. These bounds on the linear span of bent sequences are evaluated in Table 5.18 for several values of register length d. A comparison of the properties of vari- ous DS-SSMA signal sets is shown in Table 5.19. In summary, bent sequences and their generators have several desirable features: (a) optimal periodic cross-correlation properties for multiple access uses (although the choice of short periods is limited). (b) Large linear span and balance for AJ applications. (c) Easy sequence 