Consider a $2^{k} \times N$ binary matrix $A=\left\{a_{\ell, k}\right\}, a_{\ell, k} \in\{0,1\}$. For rows $i$ and $j$, let the Hamming distance be $d_{i, j}=\sum_{\ell=1}^{N}\left|a_{i, \ell}-a_{j, \ell}\right|$. Let $D_{\min }=\min _{i, j} d_{i, j}$. Then which of the following is TRUE?
Hint: Consider any block of $k-1$ columns.
- $D_{\min } \leq N-k+1$.
- $D_{\min } \leq N-k$.
- $D_{\min } \leq N-k-1$.
- $D_{\min } \leq N-k-2$.
- None of the above.