Kumar, PV; Helleseth, T; Calderbank, AR; Jr, ARH, *Large families of quaternary sequences with low correlation*,
IEEE Transactions on Information Theory, vol. 42 no. 2
(1996),
pp. 579-592 [doi] .
**Abstract:**

*A family of quaternary (Z4-alphabet) sequences of length L = T -1, size M > L2 +3X+2, and maximum nontrivial correlation parameter Cmax < 2√L + 1 + 1 is presented. The sequence family always contains the four-phase family A. When r is odd, it includes the family of binary Gold sequences. The sequence family is easily generated using two shift registers, one binary, the other quaternary. The distribution of correlation values is provided. The construction can be extended to produce a chain of sequence families, with each family in the chain containing the preceding family. This gives the design flexibility with respect to the number of intermittent users that can be supported, in a code-division multiple-access cellular radio system. When r is odd, the sequence families in the chain correspond to shortened Z4 -linear versions of the Delsarte-Goethals codes. Index Terms-. © 1996 IEEE.*