Characterizations of generators for modified de Bruijn sequences
Removing a single zero from the longest run of zeros in an order \(n\) de Bruijn sequence produces the corresponding order \(n\) modified de Bruijn sequence with the period \(2^ n-1\). The \(m\)-sequences, whose feedback function are primitive polynomials over \(GF(2)\) form a linear subset of modified de Bruijn sequences. This paper studies the nonlinear feedback function characteristics of the remaining order \(n\) modified de Bruijn sequences. These feedback functions have the form \(x_ n\oplus g(x_{n- 1},\dots,x_ 1)\) where \(\oplus\) denotes the addition over \(GF(2)\). The distribution data of the feedback function for \(4\leq n \leq b\) are presented. Some theoretical results about the weight, the number of terms and the degree of nonlinearity of the function \(g(x_{n-1},\dots,x_ 1)\) are also provided.
scientific article; zbMATH DE number 203285