Quaternary constant-amplitude codes for Multicode CDMA

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.sub.4]) of length [2.sup.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.sup.4] having the bent property, i.e., its Fourier transform has magnitudes [2.sup.m/2]. Several constructions of such functions are presented, which are exploited in connection with algebraic codes over [Z.sub.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. Index Terms--Bent function, code, code-division multiple access (CDMA), Delsarte-Goethals, Kerdock, multicode, peak-to-average power ratio (PAPR), quaternary, Reed-Muller.