Properties of the subsequences of a class of linear product sequences

The properties of the subsequences of a class of linear product shift-register sequences are studied. The particular class concerns those derived from two m sequences of relatively prime length. Expressions are presented for the moments of the subsequence weight distribution. The expressions display a systematic relationship between the moments and the characteristic polynomials of the parent msequences. The importance of correct choice of parent sequences is demonstrated by the results, which show considerable variationof M-tuple weight distribution for product sequences of the same length but having different characteristic polynomials. Consideration of the expression for third moment provides a means for selecting parent m sequences to minimise skewness of the weight distribution.