9], and linear span bounds [60], [61] are given in Section 5.10. A special DSMA PN sequence design criterion, which takes into account the effects of data modulation on sequence cross-correlations, has been studied in [31], [62], [63], [64], [90] and is useful in short period designs. Table 5.20. Additional multiple-access sequence set designs (Table 5.19 contains comparable information for the designs discussed in this book). Here N is the period of each sequence, p represents a prime number, and d is an integer. Restriction Alphabet Family Family on length N N + 1 Alltop (difference set) [65]* 2N + 1 prime 2N +1 Sarwate (FZC seq.) [64]* Prime N - 1 Blake and Mark [77] N+1 Prime (N + 1)k <1+(k+1)VN+ McGree [78] Prime Alltop (cubic phase) [65] Prime Alltop (quad. phase) [65]* Prime N - 1 Scholtz and Welch (grp. char.) [33]* Prime N - 2 N + 1 H. Trachtenberg [66] N 1=pd-1,dodd (N + 1) T. Helleseth [79] N = pd 1,pd2 # 2 mod 3 1+2VN+1 Sidelnikov [80]" N = pd 1 <1+VN+1 Kumar and Moreno [81]" N =pd-1 = <1+VN+ Kumar, Scholtz, and Welch [82]* N = p d - 1, d even N + 1 1 N +1 Suehiro and Hatori [83] N = p2 Krone and Sarwate [84]* N = pd - 1,pd = - 1 mod 4 5+3VN+1 P. Solé [85], Boztas et al. (type A) [86] N=2d 1 <1+VN+ also Udaya and Siddiqi [91] N + 2 Boztas et al. (type B) [86]* 1=2(2dd-1) <2+VN+2 Boztas and Kumar [89]* N = 2d - 1, d odd V2(N+1) No and Kumar [87]* I=22d-1 N + 1 *Sequence sets that are asymptotically optimal because they meet known correlation bounds as N goes to infinity. Pseudonoise Generators Recent applications of DSMA techniques to commercial communications has renewed interest in the design of sequence families with good correla- tion properties. Table 5.20 gives the parameters of several designs not COV- ered in this chapter, along with source references. The table is given in order of decreasing alphabet size with the sequences near the end of the list pos- sessing a considerable implementation advantage. The core material of this chapter has been based solely on the LFSR which provides a long st