OPTIMAL AND SUBOPTIMAL QUADRIPHASE SEQUENCES DERIVED FROM MAXIMAL LENGTH SEQUENCES OVER Z(4)

The paper presents families of quadriphase sequences derived from maxi mal length sequences over Z(4) having good correlation properties. The se are: (i) families of quadriphase sequences of period (2(r) - 1) fro m maximal length sequences over Z(4); each family consisting of (2(r) + 1) sequences, (ii) families of quadriphase sequences of period 2(2(r ) - 1) from interleaved maximal length sequences over Z(4); each famil y consisting of (2(r-1) + 1) sequences. Such sequences are of interest in quadriphase modulated code division multiple access communication systems, where it is desirable to have large sets of sequences that po ssess low value of theta(max), the maximum magnitude of the periodic c rosscorrelation and out of phase auto-correlation values. The sequence s over Z(4) are viewed as trace functions of appropriately chosen unit elements of Galois extension rings of Z(4) Quadriphase sequences are then obtained from Z(4) sequences, by a quadriphase mapping, Pi, from Z(4) to 4(th) roots Of unity, given by, Pi(x) = omega(x); where x is a n element of Z(4) and omega = root-1. Periodic correlation properties (correlation values and their distribution) of the quadriphase sequenc es are obtained by using an Abelian association scheme on the elements of the corresponding Galois extension ring of Z(4). The majority of t he families of sequences derived are optimal with respect to the Welch lower bound on theta(max); the rest being suboptimal with theta(max), , bounded by root 2L, where L is the period of the sequences. However nearly half of the sequences in these families are balanced.