  Quaternary sequences of both even and odd period having low autocorrelation
are studied. We construct new families of balanced quaternary sequences of odd
period and low autocorrelation using cyclotomic classes of order eight, as well
as investigate the linear complexity of some known quaternary sequences of odd
period. We discuss a construction given by Chung et al. in "New Quaternary
Sequences with Even Period and Three-Valued Autocorrelation" [IEICE Trans.
Fundamentals Vol. E93-A, No. 1 (2010)] first by pointing out a slight
modification (thereby obtaining new families of balanced and almost balanced
quaternary sequences of even period and low autocorrelation), then by showing
that, in certain cases, this slight modification greatly simplifies the
construction given by Shen et al. in "New Families of Balanced Quaternary
Sequences of Even Period with Three-level Optimal Autocorrelation" [IEEE Comm.
Letters DOI10.1109/LCOMM.2017.26611750 (2017)]. We investigate the linear
complexity of these sequences as well.
