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 Zopf₄) 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 Zopf₄ 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 Zopf₄ (in particular quaternary Reed-Muller and trace codes) to construct families of quaternary constant-amplitude codes. Mappings from binary to quaternary constant-amplitude codes are presented as well. The resulting coding options allow a rich trade-off between code rate and minimum distance.