Quaternary Constant-Amplitude Codes for Multicode CDMA
Kai-Uwe Schmidt · IEEE Transactions on Information Theory · 2009
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 value1. In this paper, quaternary constant-amplitude codes (codes overZ4) of length2mwith error-correction capabilities are studied. These codes exist for every positive integerm, while binary constant-amplitude codes cannot exist ifmis odd. Every word of such a code corresponds to a function from the binarym-tuples to Z4having the bent property, i.e., its Fourier transform has magnitudes2m/2. Several constructions of such functions are presented, which are exploited in connection with algebraic codes over Z4(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.