elligent jammers. The predetermined mapping of PN generator output to signal phase (or amplitude), required in a DSMA system to preserve the correlation properties designed into the PN generator outputs, allows the intelligent jammer to observe the PN generator output directly; hence, design characteristics such as linear span are, to some extent, more important in the DSMA case. The Hamming distance design criterion for FHMA schemes will now be for- malized. Let {f(})} represent the k-th in a set of K periodic sequences of symbols, each symbol being in one-to-one correspondence with a transmitted fre- quency, and denote the common period by N. Then the maximum self-inter- ference which a sequence in this set can encounter corresponds to the minimum Hamming distance HA defined by (5.349) where H(x,y) denotes the Hamming distance between the vectors x and y, and fk, denotes the vector of N consecutive symbols from the sequence Frequency-Hopping Multiple-Access Designs {f(k)}, beginning with the t-th symbol. Similarly the maximum interference between a pair of FH signals in the design corresponds to the minimum Hamming distance H, given by itk Ost<<N (5.350) and, therefore, a reasonable design criterion for FHMA PN generators con- sists of minimizing Hmin = min(H , Hc). (5.351) This criterion corresponds to designing cyclic codes (over large alphabets) with large minimum distance between code words. 5.8.2 A Bound on Hamming Distance Theorem 5.4 provides an upper bound on H which depends only on the sequence period and alphabet size. The approach used in deriving Theorem 5.4 can be modified to give the following bound on H. THEOREM 5.24 [11]. Let {f,1}} and {f(}}} denote sequences of period N over an alphabet A, and let fin denote the N-tuple of consecutive elements from {f,}}} beginning at element n. Let (5.352) and determine a and B from N=aA+B,0B<A. (5.353) (5.354) Proof. Following the approach of Theorem 5.4, it is easily verified that (5.355) where Ni,a is the number of occurrences of the symbol a in one period