Computation of Discrete Function Chrestenson Spectrum Using Cayley Color Graphs

A method based on eigenvalue computations is formulated for computing the Chrestenson spectrum of a discrete p-valued function. This technique is developed by rst considering an extension to the conventional approach to computing the Walsh spectrum for a binary-valued function which is then generalized to the p-valued case (where p > 2). Algebraic groups are formulated that correspond to Cayley color graphs based on the function of interest. These graphs have spectra equivalent to the Walsh or Chrestenson spectrum of the function under consideration. Because the transformation matrix is not used in any of these computations, the method provides an alternative approach for spectral computations. This work also illustrates the correspondence between algebraic group theory and discrete logic function spectral methods. This work was supported in part by the U.S. National Science Foundation under grants CCR-0000891 and CCR-0097246 and by a research grant from the Natural Sciences and Engineering Research Council of Canada.