An efficiently generated family of binary de Bruijn sequences

We study how to generate binary de Bruijn sequences efficiently from the class of simple linear feedback shift registers with function $f(x_0, x_1, \ldots, x_{n-1}) = x_0 + x_1 x_{n-1}$ for $n \geq 3$, using cycle joining method. Based on properties this LFSRs, we propose two new generic successor rules, each which produces at least $2^{n-3}$ sequences. These classes build upon a framework proposed by Gabric, Sawada, Williams and Wong in Discrete Mathematics vol. 341, no. 11, pp. 2977--2987, November 2018. Here introduce useful choices uniquely determined state devise valid rules. significantly increase number that can be generated. In class, next bit costs $O(n)$ time space fixed $n$.