ly (5.310) Applying the definition on the left side of (5.310) to (5.306) gives a general bound on correlation magnitude. (5.311) The above development suggests the following procedure for designing a set B of distinct NLFFL functions operating on identical m-sequence shift registers, to produce sequences with good periodic auto- and cross-correla- tion properties: Property P-1. Assume that the transforms of all functions in B are non-zero on the same subset I of GF(2) and are all zero outside I . Notice that <> {r(an)} is balanced, (5.312) x EGF(2d) for all reB. Hence, a set of balanced sequences will be achieved in this design if and only if 0 is not in S. Property P-2. Choose the set S (with 0 S) SO that SNS is as small as possible for all non-integer y in GF(2d). To calculate the average size of the intersection, let ai = 1 for each i for which aies, and let a = 0 otherwise. Then for y= at, we have (5.313) and bounding the maximum intersection by the average intersection gives yeGF(2d) yEGF(2) 2d - 2 (5.314) Property P-3. Design the set B of functions SO that for each r and S in B,r # s , (5.315) x EGF(2d) 1 EGF(2d) Pseudonoise Generators This orthogonality guarantees that is 1. Since in the transform domain r(1) can be viewed as a ISI-tuple, the achievable size of B is limited by ISI, i.e., B S S. (5.316) Property P-4. Design each function in B SO that its trace transform has constant magni- tude, namely 2d/SP on I by (5.309). If this objective can be achieved and if the bounds (5.314) and (5.316) can be achieved with equality, then by (5.311) it is possible to find orthogonal NLFFL functions such that (5.317) for all # 0 mod 2d 1. The final parameter, namely ISI, can be chosen with the aid of the Welch bound, which states that RTS(T)| must be on the order of 2d12 when B is large. Assuming that (5.317) is valid and tight, the Welch bound (5.241) indi- cates that 191 should be on the order of 2d2, with larger values of ISI result- ing in designs which cannot meet that bound with equality. The above design app