Autocorrelations for Boolean Functions of Noiselike Periodic Sequences

One method of generating a waveform whose correlation function resembles that of noise is by means of combinations of periodic binary sequences. In this paper the properties of the correlation function for arbitrary functions of n periodic binary sequences are investigated. An especially simple formulation is obtained when each binary variable in all the sequences has equal probability of being 0 or 1. For this case, it is shown that there are only two functions which result in a correlation function like true purely random noise. One of these two functions corresponds to addition modulo 2. Also, the correlation for the case of a random function of n sequences is derived. Finally, expressions are obtained for the number of degenerate Boolean functions.