  A constant-amplitude code is a code that reduces the peak-to-average power
ratio (PAPR) in multicode code-division multiple access (MC-CDMA) systems to
the favorable value 1. In this paper quaternary constant-amplitude codes (codes
over Z_4) of length 2^m with error-correction capabilities are studied. These
codes exist for every positive integer m, while binary constant-amplitude codes
cannot exist if m is odd. Every word of such a code corresponds to a function
from the binary m-tuples to Z_4 having the bent property, i.e., its Fourier
transform has magnitudes 2^{m/2}. Several constructions of such functions are
presented, which are exploited in connection with algebraic codes over Z_4 (in
particular quaternary Reed-Muller, Kerdock, and Delsarte-Goethals codes) to
construct families of quaternary constant-amplitude codes. Mappings from binary
to quaternary constant-amplitude codes are presented as well.
