We are given a set V of distinct binary vectors {v₁, v₂, ...v_n} each of size k.
Now you are free to chose a subset of V, S_V = {v_i1, v_i2, v_i3, ..., v_im} such that

• 1 ≤ i₁ < i₂.... < i_m ≤ n.
• No two rows should be same in the kXm matrix M = [v_i1v_i2...v_im]

We need to minimize m (the size of subset S_V). (ie the columns of M)
For eg: a vector v of size 3 can be [0, 0, 1]^T or [1, 0, 1]^T and 6 more are possible.