## Fast Reed-Muller Spectrum Computation Using Output Probabilities

### BibTeX

@MISC{Thornton_fastreed-muller,

author = {M.A. Thornton and V.S.S. Nair},

title = {Fast Reed-Muller Spectrum Computation Using Output Probabilities},

year = {}

}

### OpenURL

### Abstract

This paper presents a new methodology for the computation of the Reed-Muller spectral coefficients of a function of any fixed polarity using its OBDD representation. By using past results that allow the computations to be performed using real arithmetic, an efficient technique may be developed in the real domain with the resulting coefficients obtained by using a simple mapping relation to the GF (2) domain. These results mathematically justify the OBDD based approach developed in this work. This result is novel since it relies on the use of OBDDs and the concept of a Boolean function output probability to compute the coefficients. This approach is also very general in that it allows other types of coefficients (such as the Walsh) to be computed as well as the Reed-Muller forms with a single OBDD operation. A small example of this technique is given to illustrate the approach followed by some experimental results. I. Introduction The Reed-Muller (RM) spectrum can be used to provide i...