Let $n > 1$. For an integer $k$ with $0 \leq k \leq 2^n-2$ the cyclotomic class $C_k$ of $2$ modulo $2^n-1$ is the set given by $$C_k = \{k, k\cdot 2, k \cdot 2^2 , \ldots, k\cdot 2^{n-1} \pmod {2^n-1}\},$$where the entries are reduced modulo $2^n-1$. Note that either $C_k = C_i$ or their intersection is empty. A set $\{a_1, \ldots, a_m\}$ of integers in $[0, 2^n-1]$ is called a complete set of representatives of the classes if $C_{a_j} \neq C_{a_i}$ whenever $i \neq j$ and $$\bigcup_{i=1}^m C_{a_i} = \{0, 1, \ldots, 2^n-1\}. $$I am interested in, given $n$, efficiently computing the corresponding complete set of representatives of the cyclotomic classes. Any ideas? I'm hoping to be able to compute this for large enough $n$. Thanks! 
Efficiently compute a complete set of representatives of cyclotomic cosets of $2$ modulo $2^n-1$
efficiency