A new class of codes is defined and analyzed when applied to a communication system that sends data over a bandlimited Gaussian channel. A code word is defined as a sequence ofr-phase values and transmitted either modulated on a carrier or transformed inton = 2rsamples on a baseband channel. An algebraic procedure is used to generate the phase sequence from a set ofpequidistant angles. The baseband model is analyzed in detail and the performance is evaluated by first assuming an ideal detector and computing an error-probability bound. Takingp = 61,73, and97, codes are shown to exist that perform close to the theoretical limit. The algebraic structure of these codes much simplifies the numerical analysis. A second receiver is defined that extracts phase values out of the received waveform and then performs a suitable quantization. The degradation of this detector appears to be moderate for low information rates when evaluated forp = 61. A carrier phase-modulated system is also defined and evaluated with a performance quite similar to the baseband model.