On the Linear Complexity of the Sequences Generated by Nonlinear Filterings

A new method of analyzing the linear complexity of second-order nonlinear filterings of m-sequences that is based on the concept of regular coset is presented. The procedure considers any value of the LFSR's length L (prime or composite number). Emphasis is on the geometric interpretation of the regular cosets which produce degeneracies in the linear complexity of the filtered sequence. Numerical expressions to compute the linear complexity of such sequences are given as well as practical rules to design second-order nonlinear filterings which preserve the maximal linear complexity are stated.