Weight class distributions of de Bruijn sequences (Q1318841)

In an \(n\) stage feedback shift register, the next content of the least significant stage \(x_ 1\) is computed as \(x_ n\oplus g(x_{n- 1},\dots, x_ 1)\) for some function \(g\), where \(\oplus\) denotes modulo two additions. The weight of \(g\) is the number of times a ``1'' occurs among its \(2^{n-1}\) inputs. While the possible values of the weight of \(g\) are known, the number of functions \(g\) with prescribed weight is not. Based on theoretical results and a computer search, these numbers are found for \(n=4,5\) and 6. For \(n=7\), partial results are provided.