 of {fii}}. Assuming for simplicity that A is the set of integers, {1, 2, Al}, the max- imum choices for the symbol counts are (5.356) (5.357) Note that these maximizing counts correspond to balanced sequences. Substitution of (5.356) and (5.357) into (5.355) yields the final result. Pseudonoise Generators This bound on H for a two-sequence set also must apply for larger sets of sequences. Surprisingly, significantly larger sets can achieve this two- sequence bound with equality. This section includes two well-known FHMA PN generator designs which achieve the bound of Theorem 5.24 with equality. One approach, analyzed by Lempel and Greenberger [11], adapts an m-sequence generator for FH purposes. The second approach described here is based on the use of Reed- Solomon code words as hopping patterns [47]. (Further material on the struc- ture of Reed-Solomon codes is available in most major texts on error-correcting codes [6], [7], [40], [41], [48].) 5.8.3 An FHMA Design Employing an M-Sequence Generator Let {bn} denote an m-sequence of period q1 - 1 with elements in GF(q), and let b denote a J-tuple of consecutive elements from {bn}, beginning with the n-th element. Furthermore let s(x) denote an arbitrary one-to-one mapping of J-tuples over GF(q) onto a set of q frequencies. A set of q' sequences {f(})} of frequencies, the set indexed by the J-tuple V of elements from GF(q), can now be defined by the relation (5.358) One possible generator mechanization is shown in Figure 5.17. Notice that indexing into a particular sequence is easily accommodated in this genera- tor mechanization, and is independent of shift register initialization. FREQUENCY SYNTHESIZER (one-to-one mapping) SEQUENCE SELECTOR bn+L-l bnti-1 Figure 5.17. FH pseudonoise generator for SSMA use, based on an m-sequence design employing a q-ary shift register. All operations are in GF(q). Frequency-Hopping Multiple-Access Designs The Hamming distance between two of the sequences defined by (5.358) and calculated over a full period at a relative shift T,