Statistical properties of a class of pseudorandom sequences

The class of sequences discussed in the paper consists of those sequences which can be produced by inversion of alternate values in binary maximal-length sequences. The statistical properties of such sequences are analysed in terms of their multidimensional higher-order autocorrelation functions, and the results are compared with the statistical properties of a truly random binary sequence. The odd-order autocorrelation functions are identically zero. Some general properties of the even-order autocorrelation functions are derived. A sampled-data Laguerre filter chain is used to assess the statistical properties of some typical sequences. The paper ends with a discussion of some techniques which can be used to form multilevel sequences.