Is there a way to prove/disprove that you can always make a binary string length 2^k+k-1 that contain all permutations of binary string length k as substring?
Originally, i just want to get the shortest strings that contains all permutations of binary strings length k.
For k=2, you can get 00110 (contains 00,01,10,11 as substrings)
For k=3, you can get 0111010001 (contains 000,001,010,011,100,101,110,111 as substrings)
For k=4, you can get 0000100110101111000
(Im sorry if my english is bad T^T)