The lexicographically smallest universal cycle for binary strings with minimum specified weight

H. Fredricksen, I.J. Kessler and J. Maiorana discovered a simple but elegant construction of a universal cycle for binary strings of length n: Concatenate the aperiodic prefixes of length n binary necklaces in lexicographic order. We generalize their construction to binary strings of length n whose weights are in the range $c,c+1,\dots ,n$ by simply omitting the necklaces with weight less than c. We also provide an efficient algorithm that generates the universal cycles in constant amortized time per bit using $O(n)$ space. Our universal cycles have the property of being the lexicographically smallest universal cycle for the set of binary strings of length n with weight ≥c.