Enumeration and Generation of Peak Sidelobe Level Equivalence Classes for m-ary Phase Codes

The peak sidelobe level of the autocorrelation of a code for m-ary phase shift keying is invariant under a particular group of mappings. Thus, it suffices to search for codes having minimal peak sidelobe by testing a single representative of each equivalence class. We present a new, more efficient algorithm to find a single representative of each equivalence class for the sake of exhaustive searches. In order to validate the algorithm, we use Burnside's Lemma from group theory to enumerate the PSL equivalence classes as orbits of a group action. The closed-form expression we derive determines the minimal fraction of the search space that must be examined in an exhaustive search.