On the classification of deBruijn sequences (Q1910540)

A deBruijn sequence of order \(n\) is a binary sequence with period length \(2^n\) which contains all binary \(n\)-tupels. The binary deBruijn graph \(B_n\) is a directed graph with \(2^n\) nodes, each labeled with a unique binary \(n\)-tupel, and an edge from node \(T= (t_0, t_1,\dots, t_{n- 1})\) to node \(U= (u_0, u_1,\dots, u_{n- 1})\) if and only if \((t_1, t_2,\dots, t_{n- 1})= (u_0, u_1,\dots, u_{n- 2})\). The deBruijn sequences of order \(n\) are divided into weight classes. Certain permutations of the edges of \(B_n\) correspond to permutations of deBruijn sequences. In this paper, symmetry groups for the weight classes of the deBruijn sequences are used to subdivide them into smaller equivalence classes. These groups are given for \(n\leq 7\) when the weight is minimal or maximal.